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

##### 2 Answers

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

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