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Chapter 3: Q. 147 (page 278)

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

3x-2y=1;2x-3y=2

Short Answer

Expert verified

Neither parallel nor perpendicular.

Step by step solution

01

Step 1. Given information 

The given equations are3x-2y=1and2x-3y=2.

02

Step 2. Solve for y.

Solve both the equations to obtain the value of y in terms of x.

3x-2y=1-2y=1-3x-2y-2=1-3x-2y=-12+32x

2x-3y=2-3y=2-2x-3y-3=2-2x-3y=-23+23x

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=32m2=23

  • The obtained slopes are neither same nor negative reciprocal of each other. So, the given lines are neither parallel nor perpendicular.

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