Answer:
[tex]y= \frac{1}{5}x- \frac{56}{5} [/tex]
Step-by-step explanation:
We want to find the equation of the line that goes through: !6,-10) and is perpendicular to the line
[tex]5x + 3y = 2y - 3[/tex]
Let's simplify the equation of the line to get:
[tex]3y - 2y = - 5x + 3[/tex]
[tex]y = - 5x + 3[/tex]
The slope of this line is -5.
The perpendicular to this line has a slope of
[tex] \frac{1}{5} [/tex]
The equation going through (6,-10) is
[tex]y=m(x-x_1)+y_1[/tex]
We substitute to get;
[tex]y= \frac{1}{5} (x-6) - 10[/tex]
Expand;
[tex]y= \frac{1}{5}x- \frac{6}{5} - 10[/tex]
[tex]y= \frac{1}{5}x- \frac{56}{5} [/tex]
