# How do you write the equation in point slope form given (–2, 15), (9, –18)?

Feb 22, 2016

$y - 15 = - 3 \left(x + 2\right)$

#### Explanation:

Slope:
$\textcolor{w h i t e}{\text{XXX}} m = \frac{\Delta y}{\Delta x} = \frac{15 - \left(- 18\right)}{- 2 - 9} = \frac{33}{- 11} = - 3$

The general slope-point form for a line with slope $m$ through a point $\left(\overline{x} , \overline{y}\right)$ is
$\textcolor{w h i t e}{\text{XXX}} y - \overline{y} = m \left(x - \overline{x}\right)$

Using $\left(- 2 , 15\right)$ for $\left(\overline{x} , \overline{y}\right)$
$\textcolor{w h i t e}{\text{XXX}} y - 15 = - 3 \left(x + 2\right)$

Feb 22, 2016

Equation of the line is $3 x + y = 9$

#### Explanation:

Equation of the line between two points say $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ in point slope form is given by

$\frac{y - {y}_{1}}{x - {x}_{1}} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$, where both LHS and RHS represent slope of the line,

Hence equation of the line between $\left(- 2 , 15\right)$ and $\left(9 , - 18\right)$ is given by

$\frac{y - 15}{x - \left(- 2\right)} = \frac{\left(- 18\right) - 15}{9 - \left(- 2\right)}$ i.e.

$\frac{y - 15}{x + 2} = \frac{- 18 - 15}{9 + 2}$ or $\frac{y - 15}{x + 2} = \frac{- 33}{11} = - 3$ i.e.

$\left(y - 15\right) = - 3 \cdot \left(x + 2\right)$ i.e.

$\left(y - 15\right) = - - 3 x - 6$

or $3 x + y = - 6 + 15 = 9$

As such, equation of the line is $3 x + y = 9$