Question

How do you write an equation of a line passing through (3, -2), perpendicular to `11x-7y=9`?

Answer 1

Please see the explanation for how it is done.

`y = -7/11x - 1/11`

Explanation:

Begin by writing the given line in slope-intercept form so that you can obtain the slope, m, by observation:

`11x - 7y = 9`

`-11/7x + y = -9/7`

`y = 11/7x - 9/7`

The slope, m, of the given line is:

`m = 11/7`

The slope, n, of all lines perpendicular to the given line is:

`n = -1/m`

`n = -1/(11/7)`

`n = -7/11`

The equation of all lines perpendicular is:

`y = -7/11x + b`

To find the desired line, we substitute the given point, `(3, -2)` for x and y and then solve for b:

`-2 = -7/11(3) + b`

`-22/11 = -21/11 + b`

`-22/11 + 21/11 = b`

`b = -1/11`