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Chapter 4: Q. 4.101 (page 513)

Use slopes and y-intercepts to determine if the lines 2x+5y=5and y=-25x-4are 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:

2x+5y=5y=-25x-4

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:

5y=-2x+5y=-2x+55y=-25x+1

The second equation is already in slope-intercept form.

03

Step 3. Determine the slopes and y-intercepts.

For the first equation, m=-25and the y-intercept is (0,1).

For the second equation, m=-25and the y-intercept is (0,-4).

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

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