# How do you write an equation of a line given (9,-5), m=-1/3?

Aug 29, 2017

$y = - \frac{1}{3} x - 2$

#### Explanation:

Let the given point be ${P}_{1} \to \left(\textcolor{g r e e n}{{x}_{1}} , \textcolor{red}{{y}_{1}}\right) = \left(\textcolor{g r e e n}{9} , \textcolor{red}{- 5}\right)$

Let the gradient be $m = - \frac{1}{3}$

Using the standardised form $\textcolor{red}{{y}_{1}} = m \textcolor{g r e e n}{{x}_{1}} + c$

Where $c$ is a constant

Then by substitution: $\textcolor{red}{- 5} = \left(- \frac{1}{3}\right) \left(\textcolor{g r e e n}{9}\right) + c$

but $- \frac{1}{3} \times 9 = - 3$ giving:

$- 5 = 3 + c$

Add $\textcolor{m a \ge n t a}{3}$ to both sides

$\textcolor{g r e e n}{- 5 = - 3 + c \textcolor{w h i t e}{\text{dd")->color(white)("dd}} - 5 \textcolor{m a \ge n t a}{+ 3} = - 3 \textcolor{m a \ge n t a}{+ 3} + c}$

color(green)(color(white)("ddddddddddddd")-> color(white)("dddd")-2color(white)("d")=color(white)("dddd")0color(white)("d")+c

Thus $c = - 2$ so the finished equation is:

$y = - \frac{1}{3} x - 2$