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Chapter 3: Q. 3.41 (page 270)

Use slopes and y-intercepts to determine if the lines are parallel:

鈸� 2x+5y=5and y=-25x-4

鈸� y=-12x-1and x+2y=-2

Short Answer

Expert verified

鈸� The given lines are parallel.

鈸� The given lines are not parallel; They are the same line.

Step by step solution

01

Step 1. Given Information  

Pair of lines:

鈸� 2x+5y=5and y=-25x-4

鈸� y=-12x-1and x+2y=-2

02

Step 2. Required to find 

Use slopes and y-intercepts to determine if the lines are parallel

03

Step 3. Convert the equations into slope and y-intercept form 

If the co-efficient of y is not 1, divide the equations by the co-efficient of y, rearrange the terms to make equation of the form y=mx+b.

the equations become:

鈸� localid="1645503268542" y=-25x+1and y=-25x-4

鈸� y=-12x-1and y=-12x-1

04

Step 4. Compare the slopes and y-intercepts to determine the parallelism 

鈸� The slopes are same and y-intercepts are different. Therefore, the given lines are parallel.

鈸� The slopes are same and y-intercepts are same as well. Therefore, the given lines are not parallel; They are the same line.

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Most popular questions from this chapter

Use the slope formula to find the slope of the line between each pair of points.

3,-6,2,-2.

Find the equation of the line shown in each graph and write the equation in slope-intercept form.

In the following exercises, use slopes and y-intercepts to determine if the lines are parallel, perpendicular, or neither.

y=2and y=6

Find the equation of a line with given slope and y-intercept and write the equation in slope-intercept form.

Slope 0 and y-intercept0,-1.

In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope鈥搃ntercept form.

2x + 5y = 鈭�10, point (10, 4)
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