# How do you write an equation in slope intercept form of a line containing the coordinates (7,4) and (14,8)?

Sep 25, 2016

$y = \frac{4}{7} x$

#### 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.

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 (7 ,4) and (14 ,8)

let $\left({x}_{1} , {y}_{1}\right) = \left(7 , 4\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(14 , 8\right)$

$\Rightarrow m = \frac{8 - 4}{14 - 7} = \frac{4}{7}$

The equation can be partially written as $y = \frac{4}{7} x + b$

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

Using (7 ,4). That is x = 7 and y = 4

$\Rightarrow 4 = \left(\frac{4}{7} \times 7\right) + b \Rightarrow 4 = 4 + b \Rightarrow b = 0$

$\Rightarrow y = \frac{4}{7} x \text{ is the equation in slope-intercept form}$