To find the intercept put a 0 where the y is in the equation L = ax + by + c = 0. Also note, the a and b and c are there to represent real numbers.
ax + b0 + c = 0
ax + c = 0
ax + c - c = -c
ax = -c
ax/a = -c/a
x = -c/a
x-intercept = -c/a
To find the y-intercept put 0 were the x is located in the equation ax + by + c = 0 and do the same thing as above.
a0 + by + c =0
by + c = 0
by +c -c = 0-c
by = 0 -c
by/b = -c/b
y = -c/b
The y-intercept is at -c/b
Why does putting a 0 where the x or y is located work? Well, the x-intercept point is (x,0). In this point, you will notice the 0 is located in the y position in(x,y).So to find the x-intercept we put the 0 in the y where it is located in ax + by + c and then solve for x. This is also true for the y-intercept, which is at (0,y). The intercepts are on the axes. The y-intercetp is on the y axes at (0,y) and the x-intercept is on the x axes at (x,0)
