Question

A line passes through the points (0, 6) and (–9, 9). What is its equation in slope-intercept form?

Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

`y = -(1)/(3) x + 6`

Explanation:

Slope-intercept form:
`y = mx + b`, where
`m` is the slope and
`b` is the y-intercept.

The formula to find the slope of a line is
`m = (y_(2) - y_(1) )/(x_(2) - x_(1) )`.

1) Plug the coordinates into this
`m = (y_(2) - y_(1) )/(x_(2) - x_(1) )`.

`m = (9 -6 )/(-9 - 0 )`

2) Solve it. Simplify it if possible.

`m = (3 )/(-9)`

Simplified:
`m = (1 )/(-3 )`

3) Plug the result into
`y = mx + b`.

`y = (1)/(-3) x + b`

4) Plug one of the points (
`x_(1), y_(1)` or
`x_(2), y_(2)`) into
`y = (1)/(-3) x + b` to find
`b`.

`6 = (1)/(-3)(0) + b`

`6 = 0 + b`

`6 - 0 = b`

`6 = b`

5) Plug the result of
`b` into
`y = (1)/(-3) x + b`.

`y = (1)/(-3) x + 6`

The negative situated in the denominator can be genaralised to the fraction.

Therefore,
`y = -(1)/(3) x + 6`.