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Chapter 4: Q. 4.102 (page 513)

Use slopes and y-intercepts to determine if the lines 4x-3y=6and y=43x-1are parallel.

Short Answer

Expert verified

The lines have the same slope and different y-intercepts and so they are parallel.

Step by step solution

01

Step 1. Given information.

The given equations are:

4x-3y=6y=43x-1

02

Step 2. Write the equation in slope-intercept form.

The slope-intercept form is y=mx+b, where m is the slope and (0,b)is the y-intercept.

The first equation can be written as:

-3y=-4x+6y=-4x+6-3y=43x-2

The second equation is already in slope-intercept form.

03

Step 3. Determine the slopes and y-intercepts.

For the first equation, m=43and the y-intercept is (0,-2).

For the second equation, m=43and the y-intercept is (0,-1).

The lines have the same slope and different y-intercepts and so they are parallel.

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