# What is the equation of the line passing through (13,7) and (37,47)?

May 13, 2018

$5 x - 3 y = 44$

#### 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)

$\text{let "(x_1,y_1)=(13,7)" and } \left({x}_{2} , {y}_{2}\right) = \left(37 , 47\right)$

$\Rightarrow m = \frac{47 - 7}{37 - 13} = \frac{40}{24} = \frac{5}{3}$

$\Rightarrow y = \frac{5}{3} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

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

$\text{using "(13,7)" then}$

$7 = \frac{65}{3} + b \Rightarrow b = \frac{21}{3} - \frac{65}{3} = - \frac{44}{3}$

$\Rightarrow y = \frac{5}{3} x - \frac{44}{3} \leftarrow \textcolor{red}{\text{in slope-intercept form}}$

$\text{multiply all terms by 3 and rearrange}$

$\Rightarrow 3 y = 5 x - 44$

$\Rightarrow 5 x - 3 y = 44 \leftarrow \textcolor{red}{\text{in standard form}}$