solve for a. and b. ### Educational Content on Linear Functions#### The Graph of a Linear FunctionThe graph of a linear function $ f $ is shown below. ##### Tasks:1. **Identify the slope, y-intercept, and x-intercept.**2. **Write the equation that defines $ f $.****Identifying Key Features:**- The slope is $ \boxed{-1} $. *(Type an integer or a simplified fraction.)***Graph Explanation:**The graph displayed is a Cartesian coordinate plane with both x and y axes ranging from -10 to 10. The linear function graph is a straight line that intersects the y-axis at $ y = 8 $ and the x-axis at $ x = 8 $. **Steps to Identify:**1. **Slope (m):** - The slope of a line is calculated using the formula $ \frac{\Delta y}{\Delta x} $. - On the graph, the line goes down by 8 units vertically (change in $ y $) for every 8 units it moves horizontally (change in $ x $), giving a slope of $ \frac{-8}{8} = -1 $.2. **Y-intercept (b):** - The y-intercept is the point where the line crosses the y-axis. On this graph, the y-intercept is at $ y = 8 $.3. **X-intercept:** - The x-intercept is the point where the line crosses the x-axis. On this graph, the x-intercept is at $ x = 8 $.**Writing the Equation of the Line:**- For a linear function in the form $ y = mx + b $: - Given the slope $ m = -1 $ and the y-intercept $ b = 8 $, - The equation defining $ f $ is $ y = -x + 8 $.By understanding these key elements, students can better grasp the properties and equations of linear functions.

a. x intercept is 1 y intercept is 5 Let the points be A(1,0) , B(0,5) slope = (y2 - y1) / (x2 -…

The graph of a linear function f is shown. a. Identify the slope, y-intercept, and x-intercept. b. Write the equation that defines f. Ay 10- The slope is 6- (Type an integer or a simplified fraction.) 4- 2- to -8 64 10 -4 -8 10-

The graph of a linear function f is shown. a. Identify the slope, y-intercept, and x-intercept. b. Write the equation that defines f. Ay 10- The slope is 6- (Type an integer or a simplified fraction.) 4- 2- to -8 64 10 -4 -8 10-

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: Find n and sn If a = 5 , d = 3 , an= 50

A: Given data: The first term of an A.P is a=5. The common difference is d=3. The number of term in A.P…

Q: Solve for x A 2 B C 8. 4 D

Q: Find n and sn If a = 5 , d = 3 , an= 50

Q: Given A = bh solve for b

Q: A 39 16 32 B

A: Given: The sides of the triangle are given AB=16, BC=32, AC=39 To find the angles of the given…

Q: 2. Solve for B. 30m 18m 22m

A: It is given that, We have to find B.

Q: Simplify. - (u+3) + 2u

A: To simplify the given expression.-u+3+2u

Q: SOLVE FOR THE LENGHT OF AB

A: Concept: Similarity of triangles: It is believed that two triangles are comparable triangles, if the…

Q: (7 + 4y) in (-21 C 63 in 63 in

Q: Find B so that AB = 1 = BA, where A = 3 4 5 7

Q: Solve K= PRT for P. P=

Q: Solve for b: z = cd 18

Q: Solve for w. 38= -6w - 7w - 27

Q: 1 2 C+ 3 4 5 6 1 D= 7 8 8 5

A: The above question is based on the concept of Matrices. We have to assume C and D as the two…

Q: Give the coordinates of the point in the graph below.

A: Here red point lies at the distance of 4 from +ve x-axis and 0 from the y-axis

Q: x* – 125 = 0 3

Q: Solve for a and b. 52 R. 48 52 80 80 48 T. b.

Q: 7d a = c+b

Q: 4-y² 2-y SŠ *-* zdxdzdy

A: Given: Let I=∫02∫04-y2∫02-y z dx dz dy To Find: To evaluate the given triple integration.

Q: Solve the following equation for c. 104c-5=d

Q: . Solve. Give each solution rounded to three decimal places. Show all steps! 312 300 + 300e-0.08z…

A: Given equation is : 312=300+300e-0.08x To find the value of x.

Q: Solve. 2r + 8 4 2r - 4 2 The solution set is

Q: If a = [1, 2] and b = [2, 7], find a + 2b.

Q: Solve the equation for n ny+ zp=nq+h

Q: Solve for a 3a - 6 = 3

A: we have the equation3a-6=3add both side by 6 we get 3a-6+6=3+6solving the equation we get 3a=9

Q: Solve for b. 5 2 Part: 0/3 Part 1 of 3 Multiply both sides by 2.5 to clear fractions.

Q: √√x 11 + 7 = 19

Q: Find x if mZ1 2x+ 10 and m22 3x-6. O a. 4 Ob. 24 Oc. 42 Od. 16

Q: b n Solve for p: y

Q: a̟ = 48 and a = 24 Find a,

Q: 2. Solve for 0. 6. 10

A: The figure of the triangle is To evaluate: The value of θ

Q: Q1 The frequency equation of a 3 Degree of Freedom spring mass system (Figure Q1) is given as: m³w6…

Q: Solve for b. Use all lower case letters. -(a + b) b = S =

Q: Solve r= (b + L) for L.

A: Given, r=p3b+L

Q: MR=5(a+9) and MP=13a+42

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

solve for a. and b.

### Educational Content on Linear Functions

#### The Graph of a Linear Function

The graph of a linear function $ f $ is shown below.

##### Tasks:
1. **Identify the slope, y-intercept, and x-intercept.**
2. **Write the equation that defines $ f $.**

**Identifying Key Features:**

- The slope is $ \boxed{-1} $.
*(Type an integer or a simplified fraction.)*

**Graph Explanation:**

The graph displayed is a Cartesian coordinate plane with both x and y axes ranging from -10 to 10. The linear function graph is a straight line that intersects the y-axis at $ y = 8 $ and the x-axis at $ x = 8 $.

**Steps to Identify:**

1. **Slope (m):**
- The slope of a line is calculated using the formula $ \frac{\Delta y}{\Delta x} $.
- On the graph, the line goes down by 8 units vertically (change in $ y $) for every 8 units it moves horizontally (change in $ x $), giving a slope of $ \frac{-8}{8} = -1 $.

2. **Y-intercept (b):**
- The y-intercept is the point where the line crosses the y-axis. On this graph, the y-intercept is at $ y = 8 $.

3. **X-intercept:**
- The x-intercept is the point where the line crosses the x-axis. On this graph, the x-intercept is at $ x = 8 $.

**Writing the Equation of the Line:**
- For a linear function in the form $ y = mx + b $:
- Given the slope $ m = -1 $ and the y-intercept $ b = 8 $,
- The equation defining $ f $ is $ y = -x + 8 $.

By understanding these key elements, students can better grasp the properties and equations of linear functions.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

Solve for re 0, 7 CSC" I csc² r = 4
A =-bh 9. Solve for b. 2h 2A 2h 2A OType there to search
Solve for x and y
a2– x2 а. 2a3/3 O b. a3/2 a/3 С. d. 2a3/5
How do you solve for d) and e)?
Solve for x?
Solve.d+e=2 d−e=4 Use the substitution method.
If a + b 6 2 s ab 5 5 8 Find the values of a and b
Solve =R for K. K K =
Solve: E C m² for c.
Solve for W. | 5w +10| =5
(a) Solve the initial-value problem dy dt y = 2₁²2²-2 (b) Solve the initial-value problem dy dt = 2t, = = 2t, y(0) = -2 y(0) = 1.5 help (formulas) y = 21² +1.5 (c) Graph the two solutions found in (a) and (b). A help (formulas)