### Parallel Lines in the Coordinate Plane

Parallel lines are two lines that never intersect. In the coordinate plane, that would look like this:

If we take a closer look at these two lines, the slopes are both

This can be generalized to any pair of parallel lines. Parallel lines always have the same slope and different

What if you were given two parallel lines in the coordinate plane? What could you say about their slopes?

### Examples

#### Example 1

Find the equation of the line that is parallel to

We know that parallel lines have the same slope, so the line will have a slope of *new*

The equation of the parallel line is

#### Example 2

Are the lines

First we need to rewrite the first equation in slope-intercept form.

The slope of this line is

#### Example 3

Find the equation of the line that is parallel to

Recall that the equation of a line is *new*

The equation of parallel line is

#### Example 4

Find the equation of the lines below and determine if they are parallel.

The top line has a

For the second line, the

The lines are **parallel** because they have the same slope.

#### Example 5

Find the equation of the line that is parallel to the line through the point marked with a blue dot.

First, notice that the equation of the line is

The equation of the parallel line is

### Review

Determine if each pair of lines are parallel. Then, graph each pair on the same set of axes.

y=4x−2 andy=4x+5 y=−x+5 andy=x+1 5x+2y=−4 and5x+2y=8 x+y=6 and4x+4y=−16

Determine the equation of the line that is ** parallel** to the given line, through the given point.

y=−5x+1; (−2,3) y=23x−2; (9,1) x−4y=12; (−16,−2) - \begin{align*}3x+2y=10; \ (8, -11)\end{align*}

Find the equation of the two lines in each graph below. Then, determine if the two lines are parallel.

For the line and point below, find a parallel line, through the given point.

### Review (Answers)

To see the Review answers, open this PDF file and look for section 3.8.