The equation of a line can be written in many ways. Each of them is suited to determine some characteristic of the line. For example to determine the slope and the y-intercept of a line it is written in the form y = mx + c, where m is the slope and c is the y-intercept.
To determine the x and y intercepts of a line in the general form ax + by + c = 0, the following can be done.
ax + by + c = 0
=> ax + by = -c
divide all the terms by -c
=> (-a/c)x + (-b/c)y = 1
=> x/(-c/a) + y/(-c/b) = 1
The x-intercept here is -c/a and the y-intercept is -c/b
To find the x and y intercept of any line write the equation of the line in the form x/a + y/b = 1 which gives the x-intercept as a and the y-intercept as b