# What is the equation of the line passing through (24,18) and (9,12)?

Jun 8, 2018

$y = \frac{2}{5} x + \frac{42}{5}$

#### 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)

$\text{let "(x_1,y_1)=(24,18)" and } \left({x}_{2} , {y}_{2}\right) = \left(9 , 12\right)$

$m = \frac{12 - 18}{9 - 24} = \frac{- 6}{- 15} = \frac{2}{5}$

$y = \frac{2}{5} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

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

$\text{using "(9,12)" then}$

$12 = \frac{18}{5} + b \Rightarrow b = \frac{60}{5} - \frac{18}{5} = \frac{42}{5}$

$y = \frac{2}{5} x + \frac{42}{5} \leftarrow \textcolor{red}{\text{is equation of line}}$

Jun 8, 2018

$y = \frac{2}{5} \cdot x + \frac{42}{5}$

#### Explanation:

We get the slope as
$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{12 - 18}{9 - 24} = \frac{2}{5}$
so we have
$y = \frac{2}{5} x + n$
using
$x = 9 , y = 12$
we get
$n = \frac{42}{5}$