So the slope of the first line is 4/3. If this line is perpendicular, then you have to flip it and switch the sign (flip it n switch it (how I remember it)). So the slope of the new line is -3/4.
Then you have to plug in the point you're given and the new slope. Use y=mx+b format.
-1=-3/4*-4+b
Then solve for b.
-3/4*-4 is 3.
-1=3+b
Subtract 3 from each side.
-4=b.
So now you have the y-intercept and slope. All you have to do is plug it in.
y=-3/4x + -4 or y=-3/4 - 4
There's your answer!