The Slope-intercept form of the equation of a line is given by:
[tex]y=mx+b \\ \\ where \ m \ is \ the \ slope \ and \ b \ is \ the \ y-intercept[/tex]
There is a line that is perpendicular to the line we are looking for, so the slope is:
[tex]m_{1}=\frac{3}{4}[/tex]
For two perpendicular lines it is true that:
[tex]m_{1}m_{2}=-1 \\ \\ \therefore \frac{3}{4}m_{2}=-1 \\ \\ \therefore m_{2}=-\frac{4}{3}[/tex]
[tex]m_{2}[/tex] is the slope of the line we are looking for.
Therefore we have that:
[tex]y=-\frac{4}{3}x+b \\ \\ For \ the \ point \ (-12,10) \\ \\ 10=-\frac{4}{3}(-12)+b \\ \\ \therefore b=-6[/tex]
Finally, our line is:
[tex]\boxed{y=-\frac{4}{3}x-6}[/tex]
