Your line equation:
y = -3/4 x +5.
Slope is -3/4 and y-intercept is +5.
The perpendicular line has slope of 4/3.
Reason: the slopes of two lines are perpendicular, if their product is -1.
Hence (-3/4) x (4/3) = -1.
Let b is the y-intercept of the perpendicular line, and we know the slope is 4/3.
The equation of that line is
y = 4/3 x + b
Knowing (-3, -3) is point of the line we substitute x = -3 and y = -3 in the above equation and solve for b:
-3 = 4/3 (-3) + b; steps omitted.
...
b = 1
The equation is
y = 4/3 x + 1.
If you have any questions, let me know.
