y = mx + b
where m = slope and b = y-intercept
You're already given that the slope is 5/2, so put that for m
y = 5/2x + b
To find b, use the ordered pair you're given (-4, -3) and plug -4 for x and -3 for y and solve for b.
-3 = 5/2 * -4 + b
-3 = -10 + b
7 = b
y = 5/2x + 7