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Chapter 3: Q. 139 (page 278)

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

4x-2y=5;3x+6y=8

Short Answer

Expert verified

The given lines are perpendicular.

Step by step solution

01

Step 1. Given information

The given equations are4x-2y=5and3x+6y=8.

02

Step 2. Solve for y.

Solve both the equations to obtain the value of yin terms of x.

4x-2y=5-2y=5-4x-2y-2=5-4x-2y=-52+2x

3x+6y=86y=8-3x6y6=8-3x6y=43-12x

03

Step 3. Determine slopes.

  • Now both equations are in slope-intercept form.
  • Determine the slopes m1and m2by comparing both equations with y=mx+b.

m1=2m2=-12

  • The obtained slopes are negative reciprocal of each other. So, the given lines are perpendicular lines.
04

Step 4. Check

  • Multiply both slopes to check the answer.

m1m2=2-12=-1

  • The product of slopes is -1. So, the obtained result is correct.

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