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Chapter 4: Q. 4.108 (page 515)

Use slopes and y-intercepts to determine if the lines y=34x-3and 3x-4y=12are parallel.

Short Answer

Expert verified

The equations are not parallel because they are the same line.

Step by step solution

01

Step 1. Given information.

The given equations are:

y=34x-33x-4y=12

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 is already in slope-intercept form.

The second equation can be written as:

3x-4y=12-4y=-3x+12y=-3x+12-4y=-34x-3

03

Step 3. Determine the slopes and y-intercepts.

For the first equation, m=-34and the y-intercept is (0,-3).

For the second equation, m=-34and the y-intercept is (0,-3).

The lines have the same slope, but they also have the same y-intercepts. Their equations represent the same line. They are not parallel; they are the same line.

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