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Chapter 3: Q. 134 (page 278)

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

3x-4y=-2;y=34x-3

Short Answer

Expert verified

The given lines are parallel.

Step by step solution

01

Step 1. Given information

The given equations are3x-4y=-2 andy=34x-3.

02

Step 2. Solve for y.

The second given equation is already in the slope-intercept form, so solve the first equation for y.

3x-4y=-2-4y=-2-3x-4y-4=-2-3x-4y=12+34x

03

Step 3. Determine slope and y- intercepts.

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

m=34

  • The y-intercept of first and second line is0,12and0,-3respectively.
04

Step 4. Conclusion

Since both the lines have same slope but distinct values of y-intercepts, they are parallel.

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