# How do you find the slope that is perpendicular to the line #4x+5y= -5#?

##### 2 Answers

#### Answer:

The slope of the line perpendicular to the line

#### Explanation:

Let's start with the original equation:

From here, we can manipulate the equation into the slope-intercept form. We first move the

Next, we divide both sides by

We then simplify the right portion of the equation:

And further simplification follows:

We then rearrange the entire equation to clearly show the equation in slope-intercept form:

Now that we have the equation in slope-intercept form, we can clearly see that

From here, it is easy. The product of a slope and its perpendicular slope is always

If we set

Then, we can isolate

Thus, the slope of the line perpendicular to the line

#### Answer:

The slope that is perpendicular to the line

#### Explanation:

The slope perpendicular to a line is the opposite reciprocal of the slope of the given line.

For example, if the slope of a line is 2, the slope of a line perpendicular to the line with slope 2 must be

Because in your case the line is in standard form (i.e.

You can also find the slope,

1.

2.

3.

4.

The slope of a line perpendicular to this line must be the opposite reciprocal, so