This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to con come back to the skipped part. Consider the point and line below. Point Line (-7,1) x+y=2 Exercise (a) Write an equation of the line through the point parallel to the given line. Step 1 Two distinct non-vertical lines are parallel when their slopes are equal. Since the required line is parallel to the line x + y = 2, the slope of the required line is equal to the slope of the line x + y = 2. Begin by finding the slope of this line. The slope-intercept form of the linear equation x + y = 2 is y-2-x The slope of this line is -1 -x+2 Step 2 The required line passes through (-7, 1). Substitute the values (x₁, y₁) = (-7, 1) and m = -1 into the point-slope form of an equation. y-y₁ = m(x-x₁) Submit Skip (you cannot come back) m. |(x − ( [ >> Exercise (b) Write an equation of the line through the point perpendicular to the given line. Step 1 Two distinct non-vertical lines are perpendicular when their slopes are negative reciprocals of each other. The slope of the required line is equal to the negative reciprocal of the slope of the line x + y = 2 which was found to be -1 in part (a). The negative reciprocal of -1 is 1
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to con come back to the skipped part. Consider the point and line below. Point Line (-7,1) x+y=2 Exercise (a) Write an equation of the line through the point parallel to the given line. Step 1 Two distinct non-vertical lines are parallel when their slopes are equal. Since the required line is parallel to the line x + y = 2, the slope of the required line is equal to the slope of the line x + y = 2. Begin by finding the slope of this line. The slope-intercept form of the linear equation x + y = 2 is y-2-x The slope of this line is -1 -x+2 Step 2 The required line passes through (-7, 1). Substitute the values (x₁, y₁) = (-7, 1) and m = -1 into the point-slope form of an equation. y-y₁ = m(x-x₁) Submit Skip (you cannot come back) m. |(x − ( [ >> Exercise (b) Write an equation of the line through the point perpendicular to the given line. Step 1 Two distinct non-vertical lines are perpendicular when their slopes are negative reciprocals of each other. The slope of the required line is equal to the negative reciprocal of the slope of the line x + y = 2 which was found to be -1 in part (a). The negative reciprocal of -1 is 1
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.3: Parallel And Perpendicular Lines
Problem 31PPS
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Transcribed Image Text:This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Consider the point and line below.
Point
Line
(-7, 1)
x + y = 2
Exercise (a)
Write an equation of the line through the point parallel to the given line.
Step 1
Two distinct non-vertical lines are parallel when their slopes are equal. Since the required line is parallel to the line x + y = 2, the slope of the required line is equal to the slope of the line x + y = 2. Begin by finding the slope of this line.
The slope-intercept form of the linear equation x + y = 2 is
y = 2 x
The slope of this line is
Step 2
The required line passes through (−7, 1).
Substitute the values (X₁, Y₁) = (–7, 1) and m = − 1 into the point-slope form of an equation.
m(x − x₁)
y
y - y₁
=
-x+2
=
Submit Skip (you cannot come back)
m =
The negative reciprocal of -1 is
1
Exercise (b)
Write an equation of the line through the point perpendicular to the given line.
(x −(|
Step 1
Two distinct non-vertical lines are perpendicular when their slopes are negative reciprocals of each other. The slope of the required line is equal to the negative reciprocal of the slope of the line x + y = 2 which was found to be -1 in part (a).
))
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