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Chapter 3: Q 149. (page 278)

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

y=2and y=6

Short Answer

Expert verified

Lines y=2andy=6are parallel lines.

Step by step solution

01

Step 1. Use the definition of parallel and perpendicular lines

  • Two lines that have the same slope are called parallel lines.
  • Two lines that lie in the same plane and intersect at right angles are called perpendicular lines. The slopes of these two lines are negative reciprocals of each other. Their product is-1.
02

Step 2. Use the slope-intercept form

The slope-intercept form is y=mx+b.

We can recognize that the lines y=2and y=6are horizontal lines and their slopes are both 0.

03

Step 3. Find the y-intercept

The horizontal lines cross the y-axis at y=2and at y=6.

So the y-intercepts are (0,2)and (0,6).

The lines have the same slope and different y-intercepts.

Therefore, these lines are parallel lines.

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Most popular questions from this chapter

Graph :f(x)=-x2

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

In the following exercise, determine the most convenient method to graph each line

3x-2y=-12

Graph the equation x+y=-3using the intercepts.

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

-2,-1,6,5.
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