# How do you write an equation in point slope form that passes through Point: (1, –7); Slope: -2/3?

Jun 3, 2018

$y + 7 = - \frac{2}{3} \left(x - 1\right)$

#### Explanation:

Given a point:

$\left({x}_{1} , {y}_{1}\right) = \left(1 , - 7\right)$

and a slope:

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

Point slope form is:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

$y - \left(- 7\right) = - \frac{2}{3} \left(x - 1\right)$

$\therefore y + 7 = - \frac{2}{3} \left(x - 1\right)$

graph{y+7=-2/3(x-1) [-14.96, 5.04, -8.44, 1.56]}

Jun 3, 2018

See a solution process below:

#### Explanation:

The point-slope form of a linear equation is: $\left(y - \textcolor{b l u e}{{y}_{1}}\right) = \textcolor{red}{m} \left(x - \textcolor{b l u e}{{x}_{1}}\right)$

Where $\left(\textcolor{b l u e}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right)$ is a point on the line and $\textcolor{red}{m}$ is the slope.

Substituting the information from the problem gives:

$\left(y - \textcolor{b l u e}{- 7}\right) = \textcolor{red}{- \frac{2}{3}} \left(x - \textcolor{b l u e}{1}\right)$

$\left(y + \textcolor{b l u e}{7}\right) = \textcolor{red}{- \frac{2}{3}} \left(x - \textcolor{b l u e}{1}\right)$