How do you find equation of line passing through the point (-1, 3) with slope m=2/3?

Apr 25, 2016

$y = \frac{2}{3} x + \frac{11}{3}$

Explanation:

By defining the gradient as a constant this is a straight line graph.

Standard form equation: $\text{ } y = m x + c$

Where the gradient (slope) $\to m = \frac{2}{3}$
The line passes through the point ${P}_{1} \to \left(x , y\right) = \left(- 1 , 3\right)$

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$\textcolor{red}{\text{Determine the value of c}}$
Thus at P_1" we have "color(brown)(y=m x+ c)color(green)(" "->3=2/3(-1)+c)

$\text{ } \implies 3 = - \frac{2}{3} + c$

$\text{ } 3 + \frac{2}{3} = - \frac{2}{3} + \frac{2}{3} + c$
$\text{ } \implies \frac{11}{3} = 0 + c$
$\text{ } \textcolor{red}{c = \frac{11}{3}}$
$\textcolor{b l u e}{\text{Thus "y=mx+c" "->" } y = \frac{2}{3} x + \frac{11}{3}}$