# How do you write an equation in point-slope form for the line passing through the points (2,8) and (3,4)?

Apr 2, 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 $\left(3 , 4\right)$ and $\left(2 , 8\right)$

Slope($m$) = $\frac{8 - 4}{2 - 3}$ = $\frac{4}{-} 1$ = $- 4$

• Once the Slope is determined, pick any point on that line. Say $\left(2 , 8\right)$, 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:
$\left(y - 8\right) = \left(- 4\right) \cdot \left(x - 2\right)$

• 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 $\left(3 , 4\right)$, and substitute it in our answer.

$\left(y - 8\right) = 4 - 8 = - 4$

$\left(- 4\right) \cdot \left(3 - 2\right) = \left(- 4\right) \cdot 1 = - 4$

As the left hand side of the equation is equal to the right hand side, we can be sure that the point $\left(3 , 4\right)$ does lie on the line.

• The graph of the equation would look like this:

graph{-4x+16 [-18.51, 18.55, -9.27, 9.26]}