# How do you write the equation in slope intercept form given (3, -2), (5, 4)?

Dec 3, 2017

$y = 3 x - 11$

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{to calculate m use the "color(blue)"gradient formula}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{let "(x_1,y_1)=(3,-2)" and } \left({x}_{2} , {y}_{2}\right) = \left(5 , 4\right)$

$\Rightarrow m = \frac{4 - \left(- 2\right)}{5 - 3} = \frac{6}{2} = 3$

$\Rightarrow y = 3 x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute either of the 2 points into the}$
$\text{partial equation}$

$\text{using } \left(5 , 4\right)$

$4 = \left(3 \times 5\right) + b \Rightarrow b = 4 - 15 = - 11$

$\Rightarrow y = 3 x - 11 \leftarrow \textcolor{red}{\text{in slope-intercept form}}$