# How do you write an equation of a line passing through (0, -9), perpendicular to #7x+6y=5#?

##### 1 Answer

Three steps: 1. find the gradient of the given line, 2. find the gradient of a line perpendicular to it, 3. find the equation of a line with that second gradient that passes through the given point. Solution:

#### Explanation:

Step 1 - find the gradient of the given line:

We need to rearrange it into point-slope form,

Subtract

Divide both sides by

So the gradient of the given line is

Step 2 - find the gradient of a line perpendicular to this line:

Call the new gradient

That is, to find the gradient of a line perpendicular to another line, we change the sign and take the inverse.

In this case

The gradient of the new line we want is

Step 3 - find the equation of the new line:

We know the gradient, and we know that the line passes through the point

Therefore the overall equation of the line we want to find is: