Question

How do you find the equation of the line through the points (4,5) that is perpendicular to the line 3x-4y=7?

Answer 1

The important fact about perpendicular lines is that the slope of a line perpendicular to one line is the negative reciprocal of slope of the initial line.

Explanation:

Let's first convert to slope intercept form, `y = mx + b`. This can be done by isolating `y`.

`3x - 4y = 7`

`-4y + 7 - 3x`

`y = -7/4 + 3/4x`

`:.` The slope of this line is `3/4`. Therefore, the slope of the line perpendicular will be `-4/3`.

Now, by point slope form we have:

`y - y_1 = m(x - x_1)`

`y - 5 = -4/3(x - 4)`

`y - 5 = -4/3x + 16/3`

`y = -4/3x + 31/3`

Hopefully this helps!