# How do you write an equation of the line with (4,2);m = -5/3?

Jun 30, 2015

$y = \left(- \frac{5}{3}\right) \left(x - 4\right) + 2$
or
$3 y = 26 - 5 x$
etc.

#### Explanation:

Slope of a straight line is $m = \frac{y - \hat{y}}{x - \hat{x}}$ (by definition)

With $\left(\hat{x} , \hat{y}\right) = \left(4 , 2\right)$ and $m = \left(- \frac{5}{3}\right)$
this becomes
$\textcolor{w h i t e}{\text{XXXX}}$$- \frac{5}{3} = \frac{y - 2}{x - 4}$
which can be rewritten in numerous forms:
$\textcolor{w h i t e}{\text{XXXX}}$$\left(y - 2\right) = \left(- \frac{5}{3}\right) \left(x - 4\right)$

$\textcolor{w h i t e}{\text{XXXX}}$$y = \left(- \frac{5}{3}\right) \left(x - 4\right) + 2$

$\textcolor{w h i t e}{\text{XXXX}}$$3 y = - 5 x + 26$