# How do you write the slope intercept form of a line going through (1,3) and (3,7)?

Nov 27, 2016

$y = 2 x + 1$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and b, the y-intercept.

We require to find m and b.

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

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

The 2 points here are (1 ,3) and (3 ,7)

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

$\Rightarrow m = \frac{7 - 3}{3 - 1} = \frac{4}{2} = 2$

We can now write the partial equation as y = 2x + b

To find b, substitute either of the 2 given points into the
partial equation

Using (1 ,3) that is x = 1 and y = 3

$3 = \left(2 \times 1\right) + b \Rightarrow 3 = 2 + b \Rightarrow b = 1$

$\Rightarrow y = 2 x + 1 \text{ is the equation in slope-intercept form}$