Question

What is the equation of the line in slope -intercept from that is perpendicular to the line y=3/4x-2 and passes through the point (-12,10) ?

Answer 1

The Slope-intercept form of the equation of a line is given by:

$y=mx+b \\ \\ where \ m \ is \ the \ slope \ and \ b \ is \ the \ y-intercept$

There is a line that is perpendicular to the line we are looking for, so the slope is:

$m_{1}=\frac{3}{4}$

For two perpendicular lines it is true that:

$m_{1}m_{2}=-1 \\ \\ \therefore \frac{3}{4}m_{2}=-1 \\ \\ \therefore m_{2}=-\frac{4}{3}$

$m_{2}$ is the slope of the line we are looking for.

Therefore we have that:

$y=-\frac{4}{3}x+b \\ \\ For \ the \ point \ (-12,10) \\ \\ 10=-\frac{4}{3}(-12)+b \\ \\ \therefore b=-6$

Finally, our line is:

$\boxed{y=-\frac{4}{3}x-6}$