# How do you write the slope-intercept equation of a line with point (2,1) with slope -2/3?

Aug 13, 2016

$y = - \frac{2}{3} x + \frac{7}{3}$

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{slope-intercept form}}$ is

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where m represents the slope and b, the y-intercept.

Here we know m but have to find b.

$\textcolor{b l u e}{\text{Partial equation"" is }} y = - \frac{2}{3} x + b$

To calculate b, substitute x = 2 and y = 1 from (2 ,1) into the partial equation.

$\Rightarrow \left(- \frac{2}{3} \times 2\right) + b = 1 \Rightarrow - \frac{4}{3} + b = 1 \Rightarrow b = \frac{7}{3}$

$\Rightarrow y = - \frac{2}{3} x + \frac{7}{3} \text{ is equation in slope-intercept form}$