What is the slope-intercept form of the equation y - 7= -5/2(x+4)

The first thing I would probably do is distribute (multiply) the -5/2 into the parenthesis:

= (-5/2)x + (-20/2)

Notice how I am not putting the x into the fraction. This is to make it easier to see the slope-intercept form.

Lets simplify the (-20/2) and then add 7 to both sides:

y - 7 = (-5/2)x - 10

y = (-5/2)x - 3

Your answer would then be:

y = (-5/2)x - 3

y = mx + b

Since it is now in the requested format.