The given equation, 4x - 3y =15, is in Standard Form (that is, Ax+By=C).
Now, once and forever, convert that to slope-intercept form and find that the slope is (-A/B). For this problem, the slope is (-4/(-3)) or 4/3.
The slope of a perpendicular line is the negative reciprocal of the slope of this line. So, it is -3/4. That means that the equation of the perpendicular line, in Standard Form, is 3x + 4y = D, and we need a point to determine D. The problem gives us the point (-2,-1).
3(-2) + 4(-1) = D
-6 - 4 = D
-10 = D
The equation of the perpendicular line, in Standard Form, is (A) 3x + 4y = -10.