We can get the intercepts by isolating x and y.
4x - 3y = 17
Subtract 4x from both sides.
-3y = -4x + 17
Divide both sides by -3.
y = 4/3x - 17/3
Input 0 for x.
y = -17/3
The y-intercept is (0, -17/3)
4x - 3y = 17
Add 3y to both sides.
4x = 3y + 17
Divide both sides by 4.
x = 3/4y + 17/4
Input 0 for y.
x = 17/4, or 4.25
The x-intercept is (4.25, 0).