Question

What is the equation of the line between `(-17,14)` and `(19,6)`?

Answer 1

`y = -2/9x + 92/2`

Explanation:

First, we find the slope `m` of the line.
The slope of the line is the change in `y` per unit of change in `x`. Equivalently, this means that a line with slope `a/b` will rise `a` units as `x` increases by `b` units. Then, we can find the slope from two points with the following formula:

`m = ("change in "y)/("change in "x) = (y_2-y_1)/(x_2-x_1)`

In this case, that gives us

`m = (6-14)/(19 - (-17)) = -8/36 = -2/9`

Now, we can write the equation using the point-slope form of a line.
`y - y_1 = m(x - x_1)`

Picking either of the points will work, so let's use `(19, 6)` (as an exercise, verify that this gives the same result if you use the other point). This gives us the equation

`y - 6 = -2/9(x - 19)`

If we wish to put that into the more common slope-intercept form, we can just multiply it out and solve for `y`.

`y - 6 = -2/9x + 38/9`

`y = -2/9x + 92/2`