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Chapter 3: Q. 3.42 (page 270)

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

鈸� 4x-3y=6and y=43x-1

鈸� y=34x-3and 3x-4y=12

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� 4x-3y=6and y=43x-1

鈸� y=34x-3and 3x-4y=12

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 formy=mx+b

the equations become:

鈸� y=43x-2and y=43x-1

鈸� y=34x-3and y=34x-3

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

Find the intercepts of the equation3x-2y=12.

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.

line y = 鈭�3x + 6, point (1, 鈭�5)

Graph the equation 3x-y=-6using the intercepts.

Graph the equations y=-13x,y=-13in the same cartesian plane.

Find the intercept for the equationx-y=5.
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