To find the x and y intercepts simply substitute y = 0 and x = 0 resp. Then calculate the value of the variable that is left.
Let's find the y intercept, x = 0
5x - 15y = 120
=> -15y = 120
=> y = 120/-15
=> y = -8
To find the x intercept, y = 0
5x - 15y = 120
=> 5x = 120
=> x = 120/5
=> x = 24
Therefore the x-intercept is (24 , 0) and the y-intercept is (0, -8).
The y intercept is the value of y when x = 0.
When x = 0, the equation looks like this
-15y = 120
Divide both sides by -15 and you get
y = -8 -- that's the y intercept.
The x intercept is the value of x when y = 0
5x = 120
x = 24