Question

what is the equation in slope-intercept form for the line that passes through (3, 7) and is perpendicular to 3x-5x=8

Answer 1

Answer:

$5x + 3y = 36$

Step-by-step explanation:

First we need to rewrite 3x-5y=8 in slope-intercept form.

$y = \frac{3}{5} x - \frac{8}{5}$

The slope of this line is

$\frac{3}{5}$

The line perpendicular to this line will have a slope that is the negative reciprocal of 3/5, which is

$m = - \frac{5}{3}$

This line passes through (3,7).

The equation is given by:

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

We substitute the point and slope to get:

$y - 7 = - \frac{5}{3} (x - 3)$

We multiply through by 3 to get:

$3y - 21 = - 5(x - 3)$

Expand to obtain:

$3y - 21 = - 5x + 15$

$3y + 5x = 15 + 21$

$5x + 3y = 36$