Question

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

Answer 1

Answer:

$y-7=\frac{8}{5}(x+5)$

or

$y=\frac{8}{5} x +15$

Step-by-step 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.

$y-y_1=m(x-x_1)\\y-7=\frac{8}{5}(x--5)\\y-7=\frac{8}{5}(x+5)$

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

$y-7=\frac{8}{5}(x+5)\\y-7 = \frac{8}{5}x + 8\\y=\frac{8}{5}x +15$