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Chapter 3: Q. 140 (page 278)

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

8x-2y=7;3x+12y=9

Short Answer

Expert verified

The given lines are perpendicular.

Step by step solution

01

Step 1. Given information

The given equations are8x-2y=7and3x+12y=9.

02

Step 2. Solve for y.

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

8x-2y=7-2y=7-8x-2y-2=7-8x-2y=-72+4x

3x+12y=912y=9-3x12y12=9-3x12y=34-14x

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=4m2=-14

  • 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=4-14=-1

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

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