# Which equation represents the line that passes through (6, 7) and (3, 6)?

Dec 5, 2016

$y = \frac{1}{3} x + 5$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

To calculate m, use the $\textcolor{b l u e}{\text{gradient formula}}$

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

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

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

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

$\text{Using " m=1/3" and } \left({x}_{1} , {y}_{1}\right) = \left(3 , 6\right)$

substitute values into equation.

$y - 6 = \frac{1}{3} \left(x - 3\right) \Rightarrow y - 6 = \frac{1}{3} x - 1$

$\Rightarrow y = \frac{1}{3} x + 5 \text{ is the equation}$