# Question #4c0bb

##### 2 Answers

When given two lines in slope-intercept form:

Only the slopes play a role in determining whether the lines are parallel or perpendicular.

#### Explanation:

Two lines are parallel, if and only if their slopes are equal:

When the two slopes are equal, it can be said that the two lines belong to a **family of lines** that are parallel.

For example, we know that the two lines:

There is are two special cases for parallel lines.

1 Vertical lines are parallel; their slope is undefined and they have no y intercept. They have the form:

Any two lines of this form parallel.

2 Horizontal lines are parallel; their slope is 0. They will have different y-intercepts. They have the form:

Any two lines of this form are parallel.

NOTE: In both cases

Two lines are perpendicular, if and only if the product of their slopes is equal to -1:

When the product of the two slopes is equal to -1, it can be said that the two lines belong to a **family of lines** that are perpendicular.

For example, we know that the two lines:

There is a special case for perpendicular lines where one is a horizontal line and the other is a vertical line:

Any two lines of these forms are perpendicular.

NOTE:

Yes for parallel lines. Lines that are parallel cannot have the same y-intercept. If they do, then they are the same line. Two lines are perpendicular if the product of their slopes equal

#### Explanation:

The y-intercept is the value of

where:

Substitute

So, if the y-intercept

**Parallel Lines**

**Example: Are the following lines parallel?**

Solve for

They are the same line, so they are not parallel.

**Perpendicular Lines**

**Example: Are the following lines perpendicular?**

Multiply the slopes.

Therefore the lines are perpendicular.

Notice on the graph that the point of intersection is the y-intercept:

graph{(y-5x-8)(y+1/5x-8)=0 [-17.35, 14.67, -2.88, 13.14]}