We are asked to write the following equation in slope intercept form
5 x - 3 y = - 9
Recall that a slope-intercept form is obtained when we solve for the varaible y completely. so we start by adding 3y to both sides:
5 x = - 9 + 3 y
now add 9 to both sides
5 x + 9 = 3 y
now divide everything on the left and on the right of the equal sign by 3 in order to isolate y completely
5x / 3 + 9 / 3 = y
that means:
y = 5/3 x + 3 (using that 9/3 = 3)
So, please select the third answer in the list of options, which agrees with our finding.