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: m_{1} = -1/m_{2}, where m_{1} and m_{2} 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.

m_{1} = -1/(-1/4) Equation for perpendicular slope with -1/4 substituted for m_{2}

m_{1} = 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 - y_{1} = m(x - x_{1}) 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