Question

How do you write the slope-intercept equation for the line that is perpendicular to the line `-5x + 2y = 16` and passes through the point `(5, 7)`?

Answer 1

Use the fact that slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.

Substitute the point into the slope-intercept form to find the value of b.

Explanation:

Given: `-5x + 2y = 16`

Add 5x to both sides:

`2y = 5x + 16`

Divide both sides by 2:

`y = 5/2x+ 8`

We can observe that the slope of the line `5/2`. The slope of a line that is perpendicular is the negative reciprocal, `-2/5`

The slope-intercept form is:

`y = -2/5x+b`

To find the value of b, substitute in the point `(5,7)`:

`7= -2/5(5)+b`

`b = 9`

The equation is:

`y = -2/5x+9`