Question

write an equation of a line that is perpendicular to the given line and that passes through the given point (4,-6); m=3/5

Answer 1

Answer:

$y=-\frac{5}{3} x-\frac{42}{5}$

Step-by-step explanation:

Given the slope and another point, simply plug them into the point-slope formula to find your y-intercept.

$y-y1=m(x-x1)\\y-(-6)=\frac{3}{5} (x-4)\\y+6=\frac{3}{5} x-\frac{12}{5} \\y=\frac{3}{5} x-\frac{42}{5}$

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 $\frac{3}{5}$, the opposite is $-\frac{3}{5}$.

To find the 'reciprocal,' flip your fraction. This will make your slope $-\frac{5}{3}$.

Your final equation is:

$y=-\frac{5}{3} x-\frac{42}{5}$