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

Mar 15, 2016

$y - 8 = - \frac{1}{3} \left(x - 5\right)$

or

$y - 10 = - \frac{1}{3} \left(x + 1\right)$

#### 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}

$= \frac{8 - 10}{5 - \left(- 1\right)}$

$= \frac{- 2}{6}$

$= - \frac{1}{3}$

Now to write in point slope form, you first choose a point, $\left({x}_{1} , {y}_{1}\right)$. For simplicity, you pick either $\left(5 , 8\right)$ or $\left(- 1 , 10\right)$, 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

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

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

$y - 8 = - \frac{1}{3} \left(x - 5\right)$

or

$y - 10 = - \frac{1}{3} \left(x + 1\right)$