# How do you write the equation given (6,-3) with slope 2/3?

May 1, 2017

Equation of the line is $2 x - 3 y = 21$

#### Explanation:

The equation of a line passing through $\left({x}_{1} , {y}_{1}\right)$ having slope $m$ is $y - {y}_{1} = m \left(x - {x}_{1}\right)$.

Therefore, the equation of a line passing through $\left(6 , - 3\right)$ having slope $\frac{2}{3}$ is $y - \left(- 3\right) = \frac{2}{3} \left(x - 6\right) \mathmr{and} 3 \left(y + 3\right) = 2 \left(x - 6\right) \mathmr{and} 2 x - 3 y = 21$.

Equation of the line is $2 x - 3 y = 21$ [Ans]

May 1, 2017

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

#### Explanation:

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

color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|))
where m represents the slope and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

$\text{here " m=2/3" and } \left({x}_{1} , {y}_{1}\right) = \left(6 , - 3\right)$

$y - \left(- 3\right) = \frac{2}{3} \left(x - 6\right) \leftarrow \textcolor{red}{\text{ substitute into equation}}$

$\Rightarrow y + 3 = \frac{2}{3} \left(x - 6\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$

$\text{distribute / simplify gives an alternative version of equation}$

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

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

$\Rightarrow y = \frac{2}{3} x - 7 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$