# What is the equation in point-slope form of the line passing through (–2, 1) and (4, 13)?

Apr 5, 2015

The Point-Slope form of the Equation of a Straight Line is:

$\left(y - k\right) = m \cdot \left(x - h\right)$
$m$ is the Slope of the Line
$\left(h , k\right)$ are the co-ordinates of any point on that Line.

• To find the Equation of the Line in Point-Slope form, we first need to Determine it's Slope . Finding the Slope is easy if we are given the coordinates of two points.

Slope($m$) = $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$ where $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ are the coordinates of any two points on the Line

The coordinates given are $\left(- 2 , 1\right)$ and $\left(4 , 13\right)$

Slope($m$) = $\frac{13 - 1}{4 - \left(- 2\right)}$ = $\frac{12}{6}$ = $2$

• Once the Slope is determined, pick any point on that line. Say $\left(- 2 , 1\right)$, and Substitute it's co-ordinates in $\left(h , k\right)$ of the Point-Slope Form.

We get the Point-Slope form of the equation of this line as:

$\left(y - 1\right) = \left(2\right) \cdot \left(x - \left(- 2\right)\right)$

• Once we arrive at the Point-Slope form of the Equation, it would be a good idea to Verify our answer. We take the other point $\left(4 , 13\right)$, and substitute it in our answer.

$\left(y - 1\right) = 13 - 1 = 12$

$\left(2\right) \cdot \left(x - \left(- 2\right)\right) = \left(2\right) \cdot \left(4 - \left(- 2\right)\right) = 2 \cdot 6 = 12$

As the left hand side of the equation is equal to the right hand side, we can be sure that the point $\left(4 , 13\right)$ does lie on the line.

• The graph of the line would look like this:
graph{2x-y=-5 [-10, 10, -5, 5]}