# What is the slope intercept form of the line with a slope of -2/3  that passes through  (-5,2) ?

Mar 5, 2018

$y = - \frac{2}{3} x - \frac{4}{3}$

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{here } m = - \frac{2}{3}$

$\Rightarrow y = - \frac{2}{3} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute "(-5,2)" into the partial equation}$

$2 = \frac{10}{3} + b \Rightarrow b = \frac{6}{3} - \frac{10}{3} = - \frac{4}{3}$

$\Rightarrow y = - \frac{2}{3} x - \frac{4}{3} \leftarrow \textcolor{red}{\text{in slope-intercept form}}$

Mar 5, 2018

$y = - \frac{2}{3} x - \frac{4}{3}$

#### Explanation:

$\textcolor{b l u e}{S l o p e = m}$

$\textcolor{b l u e}{\implies - \frac{2}{3} = \frac{y - {y}_{1}}{x - {x}_{1}}}$

Here $\textcolor{red}{{x}_{1} = - 5}$

And $\textcolor{red}{{y}_{1} = 2}$

Put them in the above equation

$\textcolor{\mathmr{and} a n \ge}{\implies - \frac{2}{3} = \frac{y - 2}{x - \left(- 5\right)}}$

$\textcolor{\mathmr{and} a n \ge}{\implies - \frac{2}{3} = \frac{y - 2}{x + 5}}$

Cross-multiply

$\textcolor{p u r p \le}{\implies - 2 \left(x + 5\right) = 3 \left(y - 2\right)}$

$\textcolor{p u r p \le}{\implies - 2 x - 10 = 3 y - 6}$

$\textcolor{p u r p \le}{\implies 6 - 10 = 2 x + 3 y}$

$\textcolor{g r e e n}{\implies - 4 - 2 x = 3 y}$

$\textcolor{g r e e n}{\implies 3 y = - 2 x - 4}$

$\textcolor{g r e e n}{\implies y = - \frac{2}{3} x - \frac{4}{3}}$