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Chapter 3: Q. 148 (page 278)

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

2x+4y=3;6x+3y=2

Short Answer

Expert verified

Neither parallel nor perpendicular.

Step by step solution

01

Step 1. Given information

The given equations are2x+4y=3and6x+3y=2.

02

Step 2. Solve for y.

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

2x+4y=34y=3-2x4y4=3-2x4y=34-12x

6x+3y=23y=2-6x3y3=2-6x3y=23-2x

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=-12m2=-2

  • The obtained slopes are neither same nor negative reciprocal of each other. So, the given lines are neither parallel nor perpendicular.

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Most popular questions from this chapter

a) Graph each function. b) State its domain and range. Write the domain and range in interval notation.

f(x)=5.

Graph: f(x) = 鈭�4x 鈭� 5

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

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

Find the equation of a line with given slope and y-intercept and write the equation in slope-intercept form.

Slope 0 and y-intercept0,-1.
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