# How do you write an equation in slope intercept form given that the line passes through the points (-1,1) and (2,3)?

May 1, 2018

$y = \frac{2}{3} x + \frac{5}{3}$

#### Explanation:

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

•color(white)(x)y=mx+b

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

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(-1,1)" and } \left({x}_{2} , {y}_{2}\right) = \left(2 , 3\right)$

$\Rightarrow m = \frac{3 - 1}{2 - \left(- 1\right)} = \frac{2}{3}$

$\Rightarrow y = \frac{2}{3} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

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

$\text{using "(2,3)" then}$

$3 = \frac{4}{3} + b \Rightarrow b = \frac{9}{3} - \frac{4}{3} = \frac{5}{3}$

$\Rightarrow y = \frac{2}{3} x + \frac{5}{3} \leftarrow \textcolor{red}{\text{in slope-intercept form}}$