Explanation:
solve for y
x-4y =24
-4y = 24-x
y = x/4 - 6 slope = 1/4, the coefficient of the x term
a perpendicular line has the negative inverse, change the sign and flip the fraction upside down to get -4/1 or -4
y=-4x + b. plug in the point x=-2, y=7 to calculate b the y intercept
7=-4(-2) + b
b = 7-8 =-1
y=-4x -1 is the perpendicular line through (-2,7)
general equation in slope intercept form is y=mx +b. m=-4, b=-1