Question

How do I use an x and y-intercept to write an equation in standard form? For example, how do I use the x-intercept of 3 and y-intercept of 6 to write an equation in standard form?

Answer 1

The x-intercept of 3 is really the point (3,0) and
the y-intercept of 6 is really the point (0,6)

So you are just given two points,
find the slope, then find the equation of the line in your usual way.

Answer 2

Okay, but how can I (if I can) write an equation in standard form (ax + by = c) using the two intercepts?

Answer 3

Ahh, you mean directly?

x/3 + y/6 = 1

(in general: x/(x-intercept) + y/(y-intercept) = 1 )

once you have that, multiply each term by 6, the LCD
2x + y = 6

check if both points lie on it.
for (3,0)
2(3) + 0 = 6 , ok
for (0,6)
0 + 6 = 6 , ok

Answer 4

Thank you so much! It is surprising that my school didn't show us that method.