First, isolate the variables to either side.
4y = -7/5x -7
Second, simplify in terms of y.
y = -7/20x - 7/4
Third, plug 0 in for y to find the y intercept and factor the x side to make it simple. Then, find the value that makes the x-factor zero.
0 = (-7/4)(1/5x +1)
1/5x + 1 = 0
1/5x = -1
x = -5
The x-intercept is (-5,0)
Fourth, plug zero in for x to find the y-intercept.
y = -7/20*(0) -7/4
y = -7/4
Therefore, the y-intercept is (0,-7/4) and the x-intercept is (-5,0).