Hello, Lydia,
Given the line y = (1/2)x - 9, we want one that is perpendicular. The format is y = mx + b, where m is the slope, (1/2) in this case. The slope is the variable that will allow us to make the line perpendicular. It is convenient that this can be achieved simply by taking the negative inverse of the slope, which would be -(2/1), or -2 in this case. Rewrite the equation:
y = -2x + b
I didn't use the same value for b, because the line, although still perpendicular, may shift up or down. But we can find b (the y-intercept) by solving the equation for b, using the point that is given to be on the line (7,10).
10 = -2*7 + b
b = 24
So the equation becomes y = -2x + 24
Bob
