Answer:
The perpendicular line would be y = -1/4x + 23/4
Explanation:
In order to find the equation of this line, we first have to note that perpendicular lines have opposite and reciprocal slopes. Therefore, since the original line has a slope of 4, we know the new line will have a slope of -1/4. Now we can use that information along with the given point in point-slope form to find the equation.
y - y1 = m(x - x1)
y - 7 = -1/4(x + 5)
y - 7 = -1/4x - 5/4
y = -1/4x + 23/4