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.
$y = 2$ and $y = 6$

Short Answer

Expert verified

Lines $y = 2$ and $y = 6$ are parallel lines.

Step by step solution

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 $- 1$ .

Step 2. Use the slope-intercept form

The slope-intercept form is $y = m x + b$ .

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

Step 3. Find the y-intercept

The horizontal lines cross the $y$ -axis at $y = 2$ and 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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In the following exercises, use slopes and $y$ -intercepts to determine if the lines are parallel, perpendicular, or neither.
$y = 2$ and $y = 6$

Short Answer

Step by step solution

Step 1. Use the definition of parallel and perpendicular lines

Step 2. Use the slope-intercept form

Step 3. Find the y-intercept

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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

Step by step solution

Step 1. Use the definition of parallel and perpendicular lines

Step 2. Use the slope-intercept form

Step 3. Find the y-intercept

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Discrete Mathematics

Logic and Functions

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are parallel, perpendicular, or neither.
$y = 2$ and $y = 6$