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