Lines perpendicular to each other have slopes that are negative reciprocals of each other. The line in question is y + 2x = 1, or y = -2x +1. Clearly, the slope is -2. So the slope of the line perpendicular to this line must have a slope of +1/2
The new line passes through point ( 7, -1). So we know x = 7, y = -1, m ( the slope) has to be +1/2.
Set up the answer in point-slope method, and solve for "b"
y = mx + b, or -1 = 1/2(7) + b
We have : -1 = (1/2)(7) + b
We have -1 = 3.5 + b
b = - 4.5 So our answer is y = (1/2)x - 4.5 , which is your last choice. I guess you forgot to call it choice "d"
