To calculate the x-intercept of a line written in standard form you simply remove the "y" and solve for x. And you remove the "x" when solving for y.
y=0 , solve for x
x=0 , solve for y
Here is an example: (solving for x)
2x + 3y = 6
2x + 3(0) = 6
2x = 6
2x/2 = 6/2
x = 3
Here is an example: (solving for y)
2x + 3y = 6
2(0) + 3y = 6
3y = 6
3y/3 = 6/3
y = 2