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All Textbook Solutions for High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9
You have a gift card for a coffee shop worth $90. Each day you use the card to get a coffee for $4.10. Write an explicit formula to represent the amount of money left on the card as an arithmetic sequence. What is the value of the card after buying 8 coffees?You start a savings account with $200 and save $30 each month. Write an explicit formula to represent the amount of money you invest into your savings account as an arithmetic sequence. How much money will you have invested after 12 months?Find the third, fifth, and tenth terms of the sequence described by each explicit formula. A(n)=4+(n+1)(5)Find the third, fifth, and tenth terms of the sequence described by each explicit formula. A(n)=2+(n+1)(6)Find the third, fifth, and tenth terms of the sequence described by each explicit formula. A(n)=5.5+(n1)(2)Find the third, fifth, and tenth terms of the sequence described by each explicit formula. A(n)=3+(n1)(1.5)Find the third, fifth, and tenth terms of the sequence described by each explicit formula. A(n)=2+(n1)(5)Find the third, fifth, and tenth terms of the sequence described by each explicit formula. A(n)=1.4+(n1)(3)Find the third, fifth, and tenth terms of the sequence described by each explicit formula. A(n)=9+(n1)(8)Find the third, fifth, and tenth terms of the sequence described by each explicit formula. A(n)=2.5+(n1)(2.5)Tell whether each sequence is arithmetic. Justify your answer. If the sequence is arithmetic, write a recursive and an explicit formula to represent it. 1.6,0.8,0,0.8,Tell whether each sequence is arithmetic. Justify your answer. If the sequence is arithmetic, write a recursive and an explicit formula to represent it. 5,10,20,40,Tell whether each sequence is arithmetic. Justify your answer. If the sequence is arithmetic, write a recursive and an explicit formula to represent it. 5,13,21,29,Tell whether each sequence is arithmetic. Justify your answer. If the sequence is arithmetic, write a recursive and an explicit formula to represent it. 51,47,43,39,Tell whether each sequence is arithmetic. Justify your answer. If the sequence is arithmetic, write a recursive and an explicit formula to represent it. 0.2,0.5,0.8,1.1,Tell whether each sequence is arithmetic. Justify your answer. If the sequence is arithmetic, write a recursive and an explicit formula to represent it. 7,14,28,56,Open-Ended Write an explicit formula for the arithmetic sequence whose common difference is -2.5.Error Analysis Your friend writes A(8)=3+(8)(5) as an explicit formula for finding the eighth term of the arithmetic sequence 3,8,13,18, Describe and correct your friends error.The local traffic update is given on a radio channel every 12 minutes from 4: 00 P.M. to 6: 30 P.M. You turn the radio on at 4: 16 P.M. How long will you wait for the local traffic update?For Exercises 15, choose the correct letter: What are the next two terms of the following sequence? 3,1,5,9, A. -7,-11 B. 10,11 C. 12,15 D. 13,17For Exercises 15, choose the correct letter: What are the next two terms of the following sequence? 2,4,8,16, F. -32,-64 G. 32,-64 H. 32,64 I. 32,64For Exercises 15, choose the correct letter: What is the common difference of the following arithmetic sequence? 13,7,27,47, A. -20 B. -6 C. -4 D. 20For Exercises 15, choose the correct letter: What is the ninth term of the arithmetic sequence defined by the explicit formula A(n)=14+(n1)(2)? F. -32 G. -30 H. 2 I. 4For Exercises 15, choose the correct letter Each time a touchdown is scored in a football game, 6 points are added to the score of the scoring team. A team already has 12 points. What explicit formula represents the number of points as an arithmetic sequence? A. A(n)=12+6n C. A(n)=12+(n1)(6) B. A(n)=12(n1)(6) D. A(n)=12+(n6)A friend opens a savings account by depositing $1000. He deposits an additional $75 into the account each month. a. What is an explicit formula that represents the amount of money in the account as an arithmetic sequence? b. How much money is in the account after 18 months? Show your work.Determine whether each rate of change is constant. If it is, find the rate of change and explain what it represents.Determine whether each rate of change is constant. If it is, find the rate of change and explain what it represents.Determine whether each rate of change is constant. If it is, find the rate of change and explain what it represents.Find the slope of each line.Find the slope of each line.Find the slope of each line.Find the slope of the line that passes through each pair of points. (2,1),(0,0)Find the slope of the line that passes through each pair of points. (4,5),(6,2)Find the slope of the line that passes through each pair of points. (3,8),(7,3)Find the slope of the line that passes through each pair of points. (1,0),(4,2)Find the slope of the line that passes through each pair of points. (8,4),(63)Find the slope of the line that passes through each pair of points. (2,3),(6,5)Find the slope of each line.Find the slope of each line.Find the slope of each line.Without graphing, tell whether the slope of a line that models each situation is positive, negative, zero, or undefined. Then find the slope. The cost of tickets to the amusement park is $ 19.50 for 1 ticket and $ 78 for 4 tickets.Without graphing, tell whether the slope of a line that models each situation is positive, negative, zero, or undefined. Then find the slope. The late fee is $ 2 regardless of the number of days the movie is late.Without graphing, tell whether the slope of a line that models each situation is positive, negative, zero, or undefined. Then find the slope. On the trip, Jerry had his cruise control set at 60mi/h for 4 hours.Without graphing, tell whether the slope of a line that models each situation is positive, negative, zero, or undefined. Then find the slope. The contract states that every day past the agreed upon completion date the project is not finished, the price is reduced by $ 25.State the independent variable and the dependent variable in each situation. Then find the rate of change for each situation. Shelly delivered 12 newspapers after 20 minutes and 36 papers after 60 minutes.State the independent variable and the dependent variable in each situation. Then find the rate of change for each situation. Two pounds of apples cost $ 3.98 .$Six pounds cost $ 11.94.State the independent variable and the dependent variable in each situation. Then find the rate of change for each situation. An airplane ascended 3000 feet in 10 minutes and 4500 feet in 15 minutes.Find the slope of the line that passes through each pair of points. (5,0)(5,5)Find the slope of the line that passes through each pair of points. (2,4),(1.5,1.5)Find the slope of the line that passes through each pair of points. (4.75,3.575),(2.25,1.425)Find the slope of the line that passes through each pair of points. 14,34,12,34Find the slope of the line that passes through each pair of points. 25,37,15,47Find the slope of the line that passes through each pair of points. (3.35,6.5),(5.65,3.5)Writing Explain why the slope of a horizontal line is always zero.Writing Describe how to draw a line that passes through the origin and has a slope of 23.Each pair of points lies on a line with the given slope. Find x or y. (7,4),(3,y); slope =14Each pair of points lies on a line with the given slope. Find x or y. (5,y),(6,4); slope =0Each pair of points lies on a line with the given slope. Find x or y. (x,5,(3,6); slope =1Each pair of points lies on a line with the given slope. Find x or y. (12,9),(x,2); slope =12For Exercises 15, choose the correct letter. What is the slope of the line that passes through the points (2,5) and (1,4)? A. 3 B. 1 C. 13 D. 13For Exercises 15, choose the correct letter. A line has slope 53. Through which two points could this line pass? F. (12,13),(17,10) H. (0,7),(3,10) G. (16,15),(13,10) ।. (11,13),(8,18)For Exercises 15, choose the correct letter. The pair of points (6,y) and (10,1) lie on a line with slope 14. What is the value of y? A. 5 B. 2 C. 2 D. 5aFor Exercises 15, choose the correct letter. What is the slope of a vertical line? F. 1 G. 0 H. 1 I. undefinedShawn needs to read a book that is 374 pages long. The graph shown at the right shows his progress over the first 8 hours of reading. If he continues to read at the same rate, how many hours total will it take for Shawn to read the entire book? A. 15 hours C. 19 hours B. 17 hours D. 21 hoursRobi has run the first 4 miles of a race in 30 minutes. She reached the 6 mile point after 45 minutes. Without graphing, is the slope of the line that represents this situation positive, negative, zero, or undefined? What is the slope?Determine whether each equation represents a direct variation. If it does, find the constant of variation. 8y=2xDetermine whether each equation represents a direct variation. If it does, find the constant of variation. 3x+4y=5Determine whether each equation represents a direct variation. If it does, find the constant of variation. 12x=36yDetermine whether each equation represents a direct variation. If it does, find the constant of variation. 7+9y+7=2xDetermine whether each equation represents a direct variation. If it does, find the constant of variation. y12=12xDetermine whether each equation represents a direct variation. If it does, find the constant of variation. 5x+12.5y=0Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x=8. y=10 when x=2Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x=8 y=6 when x=18Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x=8. y=2 when x=5.Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x=8. y=9.92 when x=12.8.Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x=8. y=1.85 when x=0.925.Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x=8. y=129 when x=323.Graph each direct variation equation. y=5xGraph each direct variation equation. y=25xGraph each direct variation equation. y=34xAn equilateral triangle is a triangle with three equal sides. The perimeter of an equilateral triangle varies directly with the length of one side. What is an equation that relates the perimeter p and length l of a side? What is the graph of the equation?The amount a you fill a tub varies directly with the amount of time t you fill it. Suppose you fill 25 gallons in 5 minutes. What is an equation that relates a and t ? What is the graph of the equation?For the data in each table, tell whether y varies directly with x. If it does, write an equation for the direct variation.For the data in each table, tell whether y varies directly with x. If it does, write an equation for the direct variation.For the data in each table, tell whether y varies directly with x. If it does, write an equation for the direct variation.Suppose y varies directly with x. Write and graph a direct variation equation that relates x and y. y=6 when x=3Suppose y varies directly with x. Write and graph a direct variation equation that relates x and y. y=43 when x=4.Suppose y varies directly with x. Write and graph a direct variation equation that relates x and y. y=58 when x=12Tell whether the two quantities vary directly. Explain your reasoning. The total number of miles run and the number of miles you run per day when training for a raceTell whether the two quantities vary directly. Explain your reasoning. Jacksons age and Dylans ageTell whether the two quantities vary directly. Explain your reasoning. A recipe that calls for 2 cups of sugar for each cup of flourTell whether the two quantities vary directly. Explain your reasoning. Writing In a direct variation equation, describe how the slope of the graph of the line is related to the constant of variation.Tell whether the two quantities vary directly. Explain your reasoning. Janine gets paid $ 16.75 per hour at her job. Write a direct variation equation where h represents the number of hours she works and d represents the amount of money she earns. Graph the equation.Solve each exercise and enter your answer on the grid provided. Suppose y varies directly with x and y=14 when x=4. What is the value of y when x=6?Solve each exercise and enter your answer on the grid provided. Suppose y varies directly with x and y=25 when x=140. What is the value of x when y=36?Solve each exercise and enter your answer on the grid provided. The point (12,9) is included in a direct variation. What is the constant of variation?Solve each exercise and enter your answer on the grid provided. The equation of the line on the graph at the right is a direct variation equation. What is the constant of variation?The distance d a train travels varies directly with the amount of time t that has elapsed since departure. If the train travels 475 miles in 9.5 hours, how many miles did the train travel after 4 hours?Find the slope and y-intercept of the graph of each equation. y=3x5Find the slope and y-intercept of the graph of each equation. y=5x+13Find the slope and y-intercept of the graph of each equation. y=x1Find the slope and y-intercept of the graph of each equation. y=11x+6Find the slope and y-intercept of the graph of each equation. y=5Find the slope and y-intercept of the graph of each equation. y=12x+6Find the slope and y-intercept of the graph of each equation. y=6.75x+8.54Find the slope and y-intercept of the graph of each equation. y=23x19Find the slope and y-intercept of the graph of each equation. y=2.25Write an equation of a line with the given slope m and y-intercept b. m=1,b=3Write an equation of a line with the given slope m and y-intercept b. m=4,b=2Write an equation of a line with the given slope m and y-intercept b. m=5,b=8Write an equation of a line with the given slope m and y-intercept b. m=0.25,b=6Write an equation of a line with the given slope m and y-intercept b. m=0,b=11Write an equation of a line with the given slope m and y-intercept b. m=1,b=38Write an equation in slope-intercept form of each line.Write an equation in slope-intercept form of each line.Write an equation in slope-intercept form of each line.Write an equation in slope-intercept form of the line that passes through the given points. (3,5) and (0,4)Write an equation in slope-intercept form of the line that passes through the given points. (2,6) and (4,2)Write an equation in slope-intercept form of the line that passes through the given points. (1,3) and (3,1)Write an equation in slope-intercept form of the line that passes through the given points. (7,5) and (3,0)Write an equation in slope-intercept form of the line that passes through the given points. (10,2) and (2,2)Write an equation in slope-intercept form of the line that passes through the given points. (0,1) and (5,6)Write an equation in slope-intercept form of the line that passes through the given points. (3,2) and (1,6)Write an equation in slope-intercept form of the line that passes through the given points. (4,3) and (3,4)Write an equation in slope-intercept form of the line that passes through the given points. (2,8) and (-3,6)Graph each equation. y=x+3Graph each equation. y=4x1Graph each equation. y=x+6Graph each equation. y=3x2Graph each equation. y=5x+1Graph each equation. y=7x4Hudson is already 40 miles away from home on his drive back to college. He is driving 65mi/h. Write an equation that models the total distance d travelled after h hours. What is the graph of the equation?When Phil started his new job, he owed the company $ 65 for his uniforms. He is earning $ 13 per hour. The cost of his uniforms is withheld from his earnings. Write an equation that models the total money he has m after h hours of work. What is the graph of the equation?Find the slope and the y-intercept of the graph of each equation. y+4=6xFind the slope and the y-intercept of the graph of each equation. y+12x=4Find the slope and the y-intercept of the graph of each equation. 3y12x+6=0Find the slope and the y-intercept of the graph of each equation. y5=13(x9)Find the slope and the y-intercept of the graph of each equation. y25x=0Find the slope and the y-intercept of the graph of each equation. 2y+6a4x=0For Exercises 15, choose the correct letter. What is an equation of the line shown in the graph at the right? A. y=32x+4 C. y=23x+4 B. y=23x+4 D. y=23x+6For Exercises 15, choose the correct letter. What is an equation of the line that has slope -4 and passes through the point (-2,-5)? F. y=4x8 G. y=4x13 H. y=4x5 I. y=4x+3For Exercises 15, choose the correct letter. What is an equation of the line that passes through the points (-4,3) and (-1,6)? A. y=x7 B. y=x1 C. y=7x+1 D. y=x+7For Exercises 15, choose the correct letter. The data shown in the table is linear. Which equation models the data? F. y=12x+12 H. y=2x+9 G. y=12x+6 I. y=2x3For Exercises 15, choose the correct letter. Karissa earns $ 200 per week plus $ 25 per item she sells. Which equation models the relationship between her pay p per week and the number of items n she sells? A. p=200n+25 C. n=25p+200 Đ’. p=25n+200 D. n=200p+25What is an equation of the line that passes through (-8,2) and has slope 34? What is the graph of the equation?Write an equation of the line in point-slope form through the given point and with the given slope m (2,1);m=3Write an equation of the line in point-slope form through the given point and with the given slope m (3,5);m=2Write an equation of the line in point-slope form through the given point and with the given slope m. (4,11) ;m=34Write an equation of the line in point-slope form through the given point and with the given slope m. (0,3) ;m=23Graph each equation. y2=2(x+3)Graph each equation. y+3=2(x+1)Graph each equation. y+1=35(x+5)Write an equation in point-slope form for each line.Write an equation in point-slope form for each line.Write an equation in point-slope form for each line.Write an equation in point-slope form of the line through the given points. Then write the equation in slope-intercept form. (4,0),(2,1)Write an equation in point-slope form of the line through the given points. Then write the equation in slope-intercept form. (3,2),(5,3)Write an equation in point-slope form of the line through the given points. Then write the equation in slope-intercept form. (5,1),(3,4)Open-Ended Write an equation of a line that has a slope of 12 in each form. a. point-slope form b. slope-intercept formModel the data in each table with a linear equation in slope-intercept form. What do the slope and y-intercept represent?Model the data in each table with a linear equation in slope-intercept form. What do the slope and y-intercept represent?Graph the line that passes through the given point and has the given slope m. (3,4) ;m=6Graph the line that passes through the given point and has the given slope m (2,1),m=3Graph the line that passes through the given point and has the given slope m. (4,2) ;m=12Writing Describe what you know about the graph of a line represented by the equation y3=23(x+4).Writing Describe how you would use the point-slope form to write the equation of a line that passes through the points (-1,4) and (-3,-5) in slope-intercept form.Writing Describe how linear data given in a table can help you write an equation of a line in slope-intercept form.A sign says that 3 tickets cost $ 22.50 and that 7 tickets cost $ 52.50. Write an equation in point-slope form that represents the cost of tickets. What is the graph of the equation?For Exercises 15, choose the correct letter. Which equation is equivalent to y6=12(x+4)? A. y=6x48 C. y=12x42 B. y=6x48 D. y=12x54For Exercises 15, choose the correct letter. Which point is located on the line represented by the equation y+4=5(x3)? F(4,5) G. (5,4) H. (3,4) I. (3,4)For Exercises 15, choose the correct letter. Which equation represents the line that passes through the points (6,3) and (4,9).? A. y+4=35(x+9) C. y3=35(x+6) B. y+4=53(x+9) D. y+3=35(x6)For Exercises 15, choose the correct letter. Which equation represents the line shown in the graph? y=3x2 G. y=3x+2 H. y+4=3(x2) I. y+8=3(x2)For Exercises 15, choose the correct letter. The population of a city increases by 4000 people each year. In 2025, the population is projected to be 450,000 people. What is an equation that gives the citys population p (in thousands of people) x years after 2010? A. p=4x+450 C. p15=4(x450) B. p450=4(x15) D. p=4x+15The table shows the cost of a large cheese pizza with additional toppings on it. What is an equation in point-slope form that represents the relationship between the number of toppings and the cost of the pizza? b. What is the graph of the equation?Find the x- and y-intercepts of the graph of each equation. x+y=7Find the x- and y-intercepts of the graph of each equation. x3y=9Find the x- and y-intercepts of the graph of each equation. 2x+3y=6Find the x- and y-intercepts of the graph of each equation. 4x2y=8Find the x- and y-intercepts of the graph of each equation. 5x4y=12Find the x- and y-intercepts of the graph of each equation. 2x+7y=11Draw a line with the given intercepts. x-intercept: 4 y-intercept: 5Draw a line with the given intercepts. x-intercept: -3 y-intercept: IDraw a line with the given intercepts. x-intercept: -6 y-intercept: -8Graph each equation using x- and y-intercepts. 5x+y=10Graph each equation using x- and y-intercepts. 3x6y=12Graph each equation using x- and y-intercepts. 4x12y=24For each equation, tell whether its graph is a horizontal or a vertical line. y=2For each equation, tell whether its graph is a horizontal or a vertical line. x=0For each equation, tell whether its graph is a horizontal or a vertical line. y=0.25For each equation, tell whether its graph is a horizontal or a vertical line. x=35Graph each equation. y=6Graph each equation. x=2Graph each equation. y=7Write each equation in standard form using integers. x=3Write each equation in standard form using integers. y=x4Write each equation in standard form using integers. y4=5(x8)Write each equation in standard form using integers. y+6=3(x+1)Write each equation in standard form using integers. y=35x+2Write each equation in standard form using integers. y=12x10Write each equation in standard form using integers. y3=79(x+4)You have only nickels and dimes in your piggy bank. When you ran the coins through a change counter, it indicated you have 595 cents. Write and graph an equation that represents this situation. What are three combinations of nickels and dimes you could have?For each graph, find the x- and y-intercepts. Then write an equation in standard form using integers.For each graph, find the x- and y-intercepts. Then write an equation in standard form using integers.Find the x- and y-intercepts of the line that passes through the given points. (4,2),(5,4)Find the x- and y-intercepts of the line that passes through the given points. (1,1),(5,7)Find the x- and y-intercepts of the line that passes through the given points. (3,2),(4,10)For Exercises 14, choose the correct letter. What is y=53x6 written in standard form using integers? A. 53x+y=6 B. 5x+3y=6 C. 5x+3y=18 D. 5x+3y=6For Exercises 14, choose the correct letter. Which of the following is an equation of a vertical line? F. 4x+5y=0 G. 4=16x H. 3y=9 I. 4x+5y=1For Exercises 14, choose the correct letter. What are the x- and y-intercepts of the graph of 7x+4y=14 A. x-intercept :-7 C. x-intercept: -2 y-intercept: 4 B. x-intercept: 7 D. x-intercept: 2 y-intercept: -4 y-intercept: -3.5For Exercises 14, choose the correct letter. Cheryl is planning to spend $ 75 on a Christmas gift for her father. He needs new socks and ties. A store has socks s and ties t on sale for $ 4 and $ 11, respectively. Which equation models this situation? F. 4s+11t=75 H. s=15t+75 G. 11s+4t=75 I. t=4s11The grocery store is selling eggs for $ 2 per dozen and bacon for $ 5 per pound. You plan to spend $ 50 in food for the benefit breakfast. Write and graph an equation that represents this situation. What are three combinations of dozens of eggs and pounds of bacon you can purchase?Write an equation of the line that passes through the given point and is parallel to the graph of the given equation. (3,2);y=3x2Write an equation of the line that passes through the given point and is parallel Ito the graph of the given equation. (4,1);y=2x+14Write an equation of the line that passes through the given point and is parallel to the graph of the given equation. (8,6) ;y=14x+5Write an equation of the line that passes through the given point and is parallel to the graph of the given equation. (6,2) ;y=23x+19Write an equation of the line that passes through the given point and is parallel to the graph of the given equation. (10,5) ;y=32x7Write an equation of the line that passes through the given point and is parallel to the graph of the given equation. (3,4);y=2Determine whether the graphs of the given equations are parallel, perpendicular, or neither. Explain. y=4x+5 4x+y=13Determine whether the graphs of the given equations are parallel, perpendicular, or neither. Explain. y=79x7 y=79x+3Determine whether the graphs of the given equations are parallel, perpendicular, or neither. Explain. y=78 x=4Determine whether the graphs of the given equations are parallel, perpendicular, or neither. Explain. y=6x8 x+6y=12Determine whether the graphs of the given equations are parallel, perpendicular, or neither. Explain. 3x+6y=12 y4=12(x+2)Determine whether the graphs of the given equations are parallel, perpendicular, or neither. Explain. y=4x+12 x+4y=32Determine whether each statement is always, sometimes, or never true. Explain. Two lines with different slopes are perpendicular.The slopes of vertical lines and horizontal lines are opposite reciprocals.A vertical line is perpendicular to the x-axis.Write an equation of the line that passes through the given point and is perpendicular to the graph of the given equation. (2,1);y=2x+1Write an equation of the line that passes through the given point and is perpendicular to the graph of the given equation. (5,7);y=13x+2Write an equation of the line that passes through the given point and is perpendicular to the graph of the given equation. (3,6);x+y=4Write an equation of the line that passes through the given point and is perpendicular to the graph of the given equation. (9,3);3x+y=5Write an equation of the line that passes through the given point and is perpendicular to the graph of the given equation. (8,3);y+4=23(x2)Write an equation of the line that passes through the given point and is perpendicular to the graph of the given equation. (0,5);x6y=2Open-Ended Write the equations of three lines whose graphs are parallel to one another.Open-Ended Write the equations of two lines whose graphs are perpendicular to one another.What is the slope of a line that is perpendicular to the x-axis?What is the slope of a line that is perpendicular to the x-axis?What is the slope of a line that is parallel to the y-axis?What is the slope of a line that is perpendicular to the y-axis?On a map, Sandusky St. passes through coordinates (2,1) and (4,8). Pennsylvania Ave. intersects Sandusky St. and passes through coordinates (1,3) and (6,2). Are these streets perpendicular? Explain.Writing Explain how you can determine if the graphs of two lines are parallel or perpendicular without graphing the lines.For Exercises 15, choose the correct letter. Which equation has a graph parallel to the graph of 9x+3y=22? A. y=3x22 B. y=3x+8 C. y=13x+12 D. y=13x2For Exercises 15, choose the correct letter. Which equation has a graph perpendicular to the graph of 7x=14y8? F. y=2x7 G. y=12x+4 H. y=12x1 I. y=2x+9For Exercises 15, choose the correct letter. Which equation is the equation of a line that passes through (-10,3) and is perpendicular to y=5x7? A. y=5x+53 B. y=15x7 C. y=15x+1 D. y=15x+5For Exercises 15, choose the correct letter. Which of the following coordinates for P will make MN. perpendicular to OP in the diagram at the right? F. (2,5) H. (3,2) G. (3,6) I. (3,5)For Exercises 15, choose the correct letter. Segment XY represents the path of an airplane that passes through the coordinates (2,1) and (4,5). What is the slope of a line that represents the path of another airplane that is traveling parallel to the first airplane? A. 2 C. 12 B. 12 D. 2A city designer is drawing the road map for a new housing development. Palm St. runs through the coordinates (11,5) and (-1,1) on the map. Pepperdine St. is going to run perpendicular to Palm St. The coordinates of Pepperdine St. are (4,7) and (7, y). What is the value of y? What is the equation for the line representing Pepperdine St. in slope-intercept form?For each table, make a scatter plot of the data. Describe the type of correlation the scatter plot shows.For each table, make a scatter plot of the data. Describe the type of correlation the scatter plot shows.Use the table below and a graphing calculator for Exercises 3 through 6. Make a scatter plot of the data pairs (years since 1980, population).Use the table below and a graphing calculator for Exercises 3 through 6. Draw the line of best fit for the data.Use the table below and a graphing calculator for Exercises 3 through 6. Write an equation for the trend line.Use the table below and a graphing calculator for Exercises 3 through 6. According to the data, what will the estimated resident population in Florida be in 2020?Use the table below and a graphing calculator for Exercises 7 through 10. Make a scatter plot of the data pairs (years since 1999, revenue).Use the table below and a graphing calculator for Exercises 7 through 10. Draw the line of best fit for the data.Use the table below and a graphing calculator for Exercises 7 through 10. Write an equation for the line of best fit.Use the table below and a graphing calculator for Exercises 7 through 10. According to the data, what will the estimated gross revenue be in 2015?In each situation, tell whether a correlation is likely. If it is, tell whether the correlation reflects a causal relationship. Explain your reasoning. The number of practice free throws you take and the number of free throws you make in a gameIn each situation, tell whether a correlation is likely. If it is, tell whether the correlation reflects a causal relationship. Explain your reasoning. The height of a mountain and the average elevation of the state it is inIn each situation, tell whether a correlation is likely. If it is, tell whether the correlation reflects a causal relationship. Explain your reasoning. The number of hours worked and an employees wagesIn each situation, tell whether a correlation is likely. If it is, tell whether the correlation reflects a causal relationship. Explain your reasoning. a drop in the price of a barrel of oil and the amount of gasoline sold.Open-Ended Describe a real world situation that would show a strong negative correlation. Explain your reasoning.Writing Describe the difference between interpolation and extrapolation. Explain how both could be useful.Writing Describe how the slope of a line relates to a trend line. What does the y-intercept represent?For Exercises 1-5, choose the correct letter. For the following situation, determine if there is a correlation. If there is a correlation, is it a causal relationship? The number of hours practicing at the batting cages and your batting average A. negative correlation and a causal relationship B. positive correlation but not a causal relationship C. positive correlation and a causal relationship D. no correlationFor Exercises 1-5, choose the correct letter. When evaluating data on a scatter plot, what can be used to make predictions about the future? F. interpolation H. correlation coefficient G. extrapolation I. causationFor Exercises 1-5, choose the correct letter. Mr. Bolton has worked for the same company for 17 years. What relationship would you expect between the number of years he has been with the company and his annual salary? A. positive correlation C. no correlation B. negative correlation D. none of the aboveFor Exercises 15, choose the correct letter. A city had a population of 150,000 people in 1990. The population growth of the city is represented by the equation p=5t+150 where p is the population in thousands and t is the time in years since 1990. In what year will the population have doubled? F. 1993 G. 2000 H. 2020 I. 2030What type of correlation is represented by the data in the scatter plot? A. positive correlation C. no correlation B. negative correlation D. none of the aboveUse the scatter plot to answer the following questions. a. What is an equation of the trend line for the data? b. What would the earnings be for 40 hours worked?Describe how each graph is related to the graph of y=x.Describe how each graph is related to the graph of y=x.Describe how each graph is related to the graph of y=x.Describe how each graph is related to the graph of y=x.Graph each function by translating y=x. y=x+3Graph each function by translating y=x. y=x2Graph each function by translating y=x. y=x1.5Describe how each graph is related to the graph of y=x. 2 units downWrite an equation for each translation of y=x. 1 unit upWrite an equation for each translation of y=x. 18 units upGraph each function by translating y=x. y=x+6Graph each function by translating y=x. y=x5Graph each function by translating y=x. y=x+3.2Write an equation for each translation of y=x. left 7 unitsWrite an equation for each translation of y=x. left 12 unitWrite an equation for each translation of y=x. right 23 unitAt the right is the graph of y=x. Graph each function by translating y=x. y=x+2At the right is the graph of y=x. Graph each function by translating y=x. y=x2The table at the right shows the dosage of a certain medication for a childs weight, w. Graph the step function for this information.Reasoning Examine the expressions [mnandnm.Substitutem=2 and n=3 in each expression and simplify. Now, substitute m=3 and n=2 in each expression and simplify. Repeat this process with 3 other sets of numbers for m and n. What is your conclusion?Writing Can the absolute value of a number equal a negative number? Explain your reasoning.Graph each translation of y=x. Describe how the graph is related to the graph of y=x. y=x+32Graph each translation of y=x. Describe how the graph is related to the graph of y=x. y=x2+4For Exercises 16, choose the correct letter. Which equation represents a translation of 6 units right of y=x? A. y=x6 B. y=x6 C. y=x+6 D. y=x+6For Exercises 16, choose the correct letter. How is the graph shown at the right related to the graph of y=x? F. translated 5 units left G. translated 5 units right H. translated 5 units up I. translated 5 units downFor Exercises 16, choose the correct letter. What is the y-intercept of y=x3? A. -3 C. 13 B. 13 D. 3For Exercises 16, choose the correct letter. Which equation represents y=x translated 4 units up? F. y=x4 G. y=x4 H. y=x+4 I. y=x+4For Exercises 16, choose the correct letter. Which equation represents the graph shown at the right? A. y=x+2 C. y=x+2 B. y=x+2 D. y=x+2For Exercises 16, choose the correct letter. What is the y-intercept of y=x+8? F. 8 H. 18 G. 18 I. 8Let f(x)=x3+1 a. What is the graph of the function? b. How is the graph related to the graph of y=x?Solve each system by graphing. Check your solution. y=x+3 y=4x2