Answer:
[tex]y = - \frac{5}{3} x + 12[/tex]
Step-by-step explanation:
First, rewrite the given equation in the form of y=mx+c.
m is the gradient while c is the y-intercept.
3x-5y=8
5y= 3x -8
[tex]y = \frac{3}{5} x - \frac{8}{5} [/tex]
Thus, the gradient of the given equation is ⅗.
The product of the gradients of perpendicular lines is -1.
(gradient of line)(⅗) = -1
gradient of line= -1 ÷⅗
gradient of line= [tex] - \frac{5}{3} [/tex]
[tex]y = - \frac{5}{3} x + c[/tex]
To find the value of c, substitute a coordinate.
When x=3, y=7,
[tex]7 = - \frac{5}{3} (3) + c[/tex]
7= -5 +c
c= 7+5
c= 12
Hence, the equation of the line is [tex]y = - \frac{5}{3} x + 12[/tex].
