# How do you write an equation in slope intercept form of a line containing the points (3,7) , (6,8)?

Sep 3, 2016

$y = \frac{1}{3} x + 6$

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{slope-intercept form}}$ is.

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where m represents the slope and b, the y-intercept.

We require to find m and b. To calculate m use the $\textcolor{b l u e}{\text{gradient formula}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 coordinate points}$

The 2 points here are (3 ,7) and (6 ,8)

let $\left({x}_{1} , {y}_{1}\right) = \left(3 , 7\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(6 , 8\right)$

$\Rightarrow m = \frac{8 - 7}{6 - 3} = \frac{1}{3}$

We can write the partial equation as $y = \frac{1}{3} x + b$

To find b, substitute the coordinates of either of the 2 points into the partial equation and solve for b.

Using the point (3 ,7) that is x = 3 and y = 7

$\Rightarrow \left(\frac{1}{3} \times 3\right) + b = 7 \Rightarrow 1 + b = 7 \Rightarrow b = 6$

Thus $y = \frac{1}{3} x + 6 \text{ is equation in slope-intercept form}$