you can put this in slope intercept form,y=mx + b. b will be the y intercept and the x intercept is the value of x that you get if y=0.
5x-9 = -8y-3
5x-9+3=-8y (now divide by -8)
-(5/8)x + 6/8 = y or,
y = -(5/8)x + 3/4.
So your y intercept is 3/4 because that's what you get when you put in x=0
and your x intercept is found by setting y (the equation now that we solved for y) to 0:
-(5/8)x + 3/4 = 0
-(5/8)x = -3/4 (now multiply by -8/5 to isolate x)
x=6/5
So x: (6/5 , 0) (x value at point on graph where line crosses x axis)
y: (0, 3/4) (y value at point on graph where line crosses y axis)