I'm not understanding this at all!
Two lines are perpendicular if their slopes are opposite recipricals. That means that the equation to compare the slopes is: m1 = -1/m2, where m1 and m2 are the slopes of the two lines.
The equation for the line that is perpendicular to the line we want is y =-1/4x -5, which means its slope is -1/4.
m1 = -1/(-1/4) Equation for perpendicular slope with -1/4 substituted for m2
m1 = 4 Simplified
Now that we have the slope of the line that we want (4) and a point (-1,7), we can use point-slope formula to find the equation of the line that we want.
y - y1 = m(x - x1) Point-slope formula
y - 7 = 4(x - (-1)) Substitution
y - 7 = 4(x + 1) Subtracting a negative means adding a positive
y - 7 = 4x + 4 Distributive property
y - 7 + 7 = 4x + 4 + 7 Add 7 to each side
y = 4x + 11 Simplify