Question

How do you write an equation of a line that has a intercept of 2 and passes through (12, 4)?

Answer 1

`color(green)(x-6y=-12)`

Explanation:

If the line has a y-intercept of `2` then it passes through `(x_1,y_1)=(0,2)`
and since we are told that it also passes through `(x_2,y_2)=(12,4)`
we can write the line's equation in two-point form as:
`color(white)("XXX")(y-2)/(x-0)=(4-2)/(12-0)`

Simplifying:
`color(white)("XXX")y-2=x(1/6)`

`color(white)("XXX")6y-12=x`

or in standard form:
`color(white)("XXX")x-6y=-12`