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Chapter 3: Q. 133 (page 278)

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

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

Short Answer

Expert verified

The given lines are parallel.

Step by step solution

01

Step 1. Given information

The given equations are y=34x-3and3x-4y=-2.

02

Step 2. Solve for y.

The first given equation is already in the slope-intercept form, so solve the second 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,-3and0,12respectively.
04

Step 4. Conclusion

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

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Most popular questions from this chapter

Find the intercepts of the equation2x+5y=10.

For the function hx=2x+1, evaluate the function.

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Find the equation of the line shown in each graph and write the equation in slope-intercept form.

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