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Given the equation
-2y + x = 2y - 8
we can find the intercepts, by letting the other variable go to zero.
For example, if we want the x-intercept, let y become zero, and we get
0 + x = 0 - 8
x = -8
If we want the y-intercept, we let x be zero, and get
-2y + 0 = 2y - 8
-4y = -8
y = 2