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Chapter 3: Q. 141 (page 278)

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

3x-6y=12;6x-3y=3

Short Answer

Expert verified

Neither parallel nor perpendicular.

Step by step solution

01

Step 1. Given information

The given equations are3x-6y=12and6x-3y=3.

02

Step 2. Solve for y.

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

3x-6y=12-6y=12-3x-6y-6=12-3x-6y=-2+12x

6x-3y=3-3y=3-6x-3y-3=3-6x-3y=-1+2x

03

Step 3. Determine slope.

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

m1=12

m2=2

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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