Question

How do you write the equation in point slope form given (-1,10) and (5,8)?

Answer 1

`y - 8 = -1/3 (x - 5)`

or

`y - 10 = -1/3 (x + 1)`

Explanation:

You already have the "point" part, now we just need to settle the "slope" part.

The slope of the straight line is a measure of how much the vertical component (`y`) changes for every unit that the horizontal component (`x`) changes. For example. a slope of `2` means that for every one unit increment in `x`, there will be a `2` units increment in `y`.

A large slope value corresponds to a steep one. A slope of `3` is steeper than a slope of `2`.

Slopes can also be negative; it just means that as `x` increases, `y` decreases. A line with a slope of `-2` means that every increment of `1` unit in `x` results in a decrease of `2` units in `y`.

Straight lines with positive slope run from the bottom-left of the graph to the top-right, while straight lines with negative slope run from the top-left of the graph to the bottom-right.

To calculate the slope, `m`, of a line from 2 points, we need to compare the change in the `y` value to the change in the `x` value

`m = frac{"Change in " y}{"Change in " x}`

`= frac{8-10}{5-(-1)}`

`= frac{-2}{6}`

`= -frac{1}{3}`

Now to write in point slope form, you first choose a point, `(x_1,y_1)`. For simplicity, you pick either `(5,8)` or `(-1,10)`, but any other point on the line will also give you a "different" but correct answer. With the gradient `m`, you just have to write

`y - y_1 = m (x - x_1)`

So using the two points above as examples. The answer is

`y - 8 = -1/3 (x - 5)`

or

`y - 10 = -1/3 (x + 1)`