Question

Write the equation of the line yhat is perpendicular to 5x+8y=16 and passes through (-5,7)

Answer 1

`y-7=(8)/(5)(x+5)`

or

`y=(8)/(5) x +15`

Explanation:

To write the equation, convert the line to slope intercept form to find the slope.

5x+8y=16

8y=16-5x

y=-5/8 x +2

The slope of this line is -5/8. The slope of the line perpendicular to this line will be the negative reciprocal or 8/5.

Write the equation using the slope m=8/5 and the point slope form.

`y-y_1=m(x-x_1)\\y-7=(8)/(5)(x--5)\\y-7=(8)/(5)(x+5)`

This is the equation of the line. You can convert it to slope intercept form:

`y-7=(8)/(5)(x+5)\\y-7 = (8)/(5)x + 8\\y=(8)/(5)x +15`