Answer:
[tex]y=-\frac{5}{3} x-\frac{42}{5}[/tex]
Step-by-step explanation:
Given the slope and another point, simply plug them into the point-slope formula to find your y-intercept.
[tex]y-y1=m(x-x1)\\y-(-6)=\frac{3}{5} (x-4)\\y+6=\frac{3}{5} x-\frac{12}{5} \\y=\frac{3}{5} x-\frac{42}{5}[/tex]
Now that we've found your y-intercept, we have the original equation. To find the perpendicular equation, you need the opposite reciprocal of your slope.
To find the 'opposite,' change your slope's sign. Since your slope is positive [tex]\frac{3}{5}[/tex], the opposite is [tex]-\frac{3}{5}[/tex].
To find the 'reciprocal,' flip your fraction. This will make your slope [tex]-\frac{5}{3}[/tex].
Your final equation is:
[tex]y=-\frac{5}{3} x-\frac{42}{5}[/tex]
