Question

Tayler claims that when a linear equation is written in general form, Ax + By + C = 0, the intercept of the corresponding graph is always -c/a.

Show that Tayler’s claim is true for the equation 3x + 5y + 45 = 0.

I am kind of confused with general form, could someone please explain to me what her claim means exactly? Thanks!

Answer 1

General form is the form Taylor listed - Ax+By+C=0.

Her claim is a little unclear, because she doesn't specify if we're considering the x-intercept or the y-intercept. However, it is true for the x-intercept. We can prove this for all cases, since if her statement is true for every line, it is definitely true for the one mentioned.

The x-intercept is the point at which y=0, so we have:

Ax+B*0+C=0

Ax+C=0

Subtracting C from both sides, we have:

Ax=-C

Dividing both sides by A, we have:

x=-C/A

Therefore, the x-intercept of all such lines is -C/A, so the x-intercept of the given line is -C/A. We can check this by substituting 0 for y in the given equation:

3x+45=0

Subtracting 45 and dividing by 3, we see that x=-15. -C/A is -45/3=-15, so this result works.