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Chapter 3: Q. 144 (page 278)

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

5x-2y=11;5x-y=7

Short Answer

Expert verified

Neither parallel nor perpendicular.

Step by step solution

01

Step 1. Given information

The given equations are5x-2y=11and5x-y=7.

02

Step 2. Solve for y.

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

5x-2y=11-2y=11-5x-2y-2=11-5x-2y=-112+52x

5x-y=7-y=7-5x-y-1=7-5x-1y=-7+5x

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=52m2=5

04

Step 4. Conclusion 

Since both the lines have different slopes which are not negative reciprocals of each other, so they are neither parallel nor perpendicular to each other.

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