Question

How do you write an equation of a line given (8,5) (-4,7)?

Answer 1

`y=-1/6x+19/3`

Explanation:

The slope-intercept form of a line is `y=mx+b` where `m` is the slope of the line and `b` is the y-intercept.
To solve for the slope, take the rise over run (change in y/change in x), or `(5-7)/(8--4)`. Keep in mind that it doesn't matter the order you subtract the 2 points as long as you keep it straight.
The slope (simplified) is `m=-1/6`.

Now we solve for b. Take either point (it doesn't matter which) and the slope and plug it into the formula `y=mx+b`.
Using point (8,5):
`5=(-1/6)(8)+b`
Now solve for `b` and get `b=19/3`.
We have everything we need for the equation, so just plug all the pieces in: `y=-1/6x+19/3`