The general layout of the slope intercept form is y = mx + b this is the form you are looking for.
Begin with the point slope form y – y1 = m(x – x1)
Your two points are (-4,-3) and -1/2 is your slope. Remember that your points are (x1,y1)
So you would plug in the -4 where the y1 is and plug in -3 where the x1 is
Your equation should now look like this: y – (-3) = -1/2(x – (-4))
Work this out by multiplying (remember a negative times a negative is a positive: y + 3 = -1/2(x + 4)
Then break it down further by multiply -1/2 to x + 4: y + 3 = -1/2x – 2
Now to put it into slope intercept form y = mx – y by distributing the equation.
Subtract 3 from each side to leave y by itself. y + 3 = -1/2x - 2
Once you subtract the 3 from both sides you have your slope intercept form; y = -1/2x - 5

Since you are given a point and the slope, you can write the equation in point-slope form first, and then convert it to slope intercept form.

y + 3 = (-1/2)(x + 4)

Distribute,

y + 3 = (-1/2)x - 2

Add -3 to both sides,

y = (-1/2)x - 5 <== Answer