# How do you write an equation in point slope and slope intercept form given (1, 2) and (2, 5)?

May 23, 2018

$y - 2 = 3 \left(x - 1\right) \text{ and } y = 3 x - 1$

#### Explanation:

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

•color(white)(x)y-y_1=m(x-x_1)

$\text{where m is the slope and "(x_1,y_1)" a point on the line}$

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(1.2)" and } \left({x}_{2} , {y}_{2}\right) = \left(2 , 5\right)$

$m = \frac{5 - 2}{2 - 1} = 3$

$\text{using "m=3" and "(x_1,y_1)=(1,2)" then}$

$y - 2 = 3 \left(x - 1\right) \leftarrow \textcolor{red}{\text{in point-slope form}}$

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

•color(white)(x)y=mx+b

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

$\text{distributing and rearranging gives}$

$y - 2 = 3 x - 3$

$y = 3 x - 1 \leftarrow \textcolor{red}{\text{in slope-intercept form}}$