How to write an equation for passing through (-7, - 4), perpendicular to y=1/2x + 9?

You would use the slope-intercept form y-y1=m (x-x1)

In this case, - 7 would be x1, and - 4 would be y1.

y - (-7) = m (x - (-4))

which would turn to y+7=m (x+4)

In order to be perpendicular, the slope, m, would have to be the negative reciprocal of 1/2, which is - 2.

y+7=-2 (x+4)

y+7=-2x-8

-7 - 7

y=-2x-15