# How do you write an equation in point slope form given slope 2/3, (5,6)?

Sep 3, 2016

The linear equation in point slope form is $y - 6 = \frac{2}{3} \left(x - 5\right)$.

#### Explanation:

The general equation for a line in point slope form is $y - {y}_{1} = m \left(x - {x}_{1}\right)$, where $m = \text{slope"=2/3}$, ${x}_{1} = 5$, and ${y}_{1} = 6$.

To get the point slope form for the variables given, plug the known values into the equation.

$y - 6 = \frac{2}{3} \left(x - 5\right)$

## ________

Now, if you wish, you can determine the slope intercept form for easier graphing, by solving the point slope form for $y$. This will give the x and y interceptss, where the x-intercept is the value of $x$ when $y = 0$, and the y-intercept is the value of $y$ when $x = 0$. Once you have the x and y intercepts, you only need to plot two points to graph the line.

The general equation for the slope intercept form is $y = m x + b$, where $m$ is the slope, $\left(\frac{2}{3}\right)$, and $b$ is the y-intercept.

Start with the point slope form and solve for $y$.

$y - 6 = \frac{2}{3} \left(x - 5\right)$

Add $6$ to both sides.

$y = \frac{2}{3} \left(x - 5\right) + 6$

Simplify.

$y = \frac{2}{3} x - \frac{10}{3} + 6$

Multiply $6$ by $\frac{3}{3}$ to get $\frac{18}{3}$.

Simplify.

$y = \frac{2}{3} x - \frac{10}{3} + \frac{18}{3}$

Simplify.
The slope intercept form is $y = \frac{2}{3} x + \frac{8}{3}$, where the slope, $m$, is $\frac{2}{3}$, and the y-intercept is $\frac{8}{3}$ and the point is $\left(0 , \frac{8}{3}\right)$.

To find the x-intercept , make $y = 0$ and solve for $x$.

$0 = \frac{2}{3} x + \frac{8}{3}$

$- \frac{2}{3} x = \frac{8}{3}$

$- 6 x = 24$

$x = \frac{24}{- 6}$

$x = - 4$

The x-intercept is $- 4$ and the point is $\left(- 4 , 0\right)$.

graph{y=2/3x+8/3 [-10, 10, -5, 5]}