How do you write an equation of a line passing through (0, -9), perpendicular to #7x+6y=5#?
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:
Step 1 - find the gradient of the given line:
We need to rearrange it into point-slope form,
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: