# How do you write an equation given points (1,2), (3,8)?

Nov 10, 2016

$y = 3 x - 1$

#### 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 gradient and b, the y-intercept.

We have to find m and b.

To find 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 $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 coordinate points}$

The 2 points here are (1 ,2) and (3 ,8)

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

$\Rightarrow m = \frac{8 - 2}{3 - 1} = \frac{6}{2} = 3$

We can write the partial equation as y = 3x + b

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

Using (1 ,2), that is x = 1 and y = 2.

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

$\Rightarrow y = 3 x - 1 \text{ is the equation}$