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Chapter 3: Q. 136 (page 278)

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

8x+6y=6;12x+9y=12

Short Answer

Expert verified

The given lines are parallel.

Step by step solution

01

Step 1. Given information 

The given equations are8x+6y=6and12x+9y=12.

02

Step 2. Solve for y.

Solve both the equations to obtain the value of yin terms of x.

8x+6y=66y=6-8x6y6=6-8x6y=1-43x

12x+9y=129y=12-12x9y9=12-12x9y=43-43x

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=-43

  • The y-intercept of first and second line is 0,1and0,43respectively.
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

In the following exercises, graph each function state its domain and range. Write the domain and range in interval notation.

f(x)=|x|+1

Graph the linear equationsy=-12x,y=-12.

Use the slope formula to find the slope of the line between each pair of points.

3,-6,2,-2.

In the following exercise, use the graph of the function to find its domain and range. Write the domain and range in interval notation.

Find the equation of a line with a given slope andy-intercept and Write the equation in slope-intercept form.

slope 15and y-intercept 0,-5.
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