Answer:
[tex]5x + 3y = 36[/tex]
Step-by-step explanation:
First we need to rewrite 3x-5y=8 in slope-intercept form.
[tex]y = \frac{3}{5} x - \frac{8}{5} [/tex]
The slope of this line is
[tex] \frac{3}{5} [/tex]
The line perpendicular to this line will have a slope that is the negative reciprocal of 3/5, which is
[tex]m = - \frac{5}{3} [/tex]
This line passes through (3,7).
The equation is given by:
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the point and slope to get:
[tex]y - 7 = - \frac{5}{3} (x - 3)[/tex]
We multiply through by 3 to get:
[tex]3y - 21 = - 5(x - 3)[/tex]
Expand to obtain:
[tex]3y - 21 = - 5x + 15[/tex]
[tex]3y + 5x = 15 + 21[/tex]
[tex]5x + 3y = 36[/tex]
