Question

How do you find the equation in slope - intercept form, of the line passing through the points (2,-3) & (-6,-7)?

Answer 1

`2 -(-6) =8`, meaning difference in `x` is `8`
`-3 - (-7) =4`, meaning difference in `y` is `4`

Explanation:

The slope intercept form is

`y=mx+b`

We're looking for `m`, the slope. The slope is rise over run, or change in `y`, `Deltay`, over change in `x`, `Deltax`, so if `Deltay=4` and `Deltax=8`, the slope is

`m = 4/8`

Simplify and it becomes `1/2`, so there's `m`.

`y=1/2x+b`

We need `b`.

Subtract `2` from `x` in the first point, and subtract `1` from `y`, which is the equivalent of moving to the adjacent point on the graph.

That gives you `(0,-4)`, so your final equation is

`y = 1/2x - 4`

(Sorry if this is confusing ;3;)