The equation of our line is y = 4x - 32.
To begin to solve this question, we must first find the slope of our line. Since it is perpendicular to the line, the slope of our line is the opposite reciprocal. The opposite reciprocal of -1/4 is 4, so the slope of our line is 4.
That means that so far, our line is y = 4x + b. Now, we need to input the values of the point we know our line goes through. Inputting 7 for x and -4 for y, we get:
-4 = 28 + b
b = -32
That means that the equation of our line is y = 4x - 32.