How do you write an equation of a line given (-1, 3) with slope m=2/3?

Dec 17, 2016

$y - 3 = \frac{2}{3} \left(x + 1\right)$ or $y = \frac{2}{3} x + \frac{11}{3}$

Explanation:

To complete this problem we use the point-slope formula.

The point-slope formula states: $\textcolor{red}{\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)}$
Where $\textcolor{red}{m}$ is the slope and $\textcolor{red}{\left({x}_{1} , {y}_{1}\right)}$ is a point the line passes through.

Substituting the information given in the problem produces the equation:

$y - 3 = \frac{2}{3} \left(x - - 1\right)$

$y - 3 = \frac{2}{3} \left(x + 1\right)$

Converting this to the more familiar slope-intercept form would give us:

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

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

$y - 0 = \frac{2}{3} x + \frac{2}{3} + \frac{9}{3}$

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