# How do you write an equation is in point-slope form for the given point (1,-7) slope -2/3?

Oct 29, 2016

The equation of this line in point-slope form is $y + 7 = \frac{- 2}{3} \left(x - 1\right)$.

#### Explanation:

The point-slope form of a linear equation is $y - {y}_{1} = m \left(x - {x}_{1}\right)$ where $m$ is the slope of the line and $\left({x}_{1} , {y}_{1}\right)$ is a point on the line. Since we have both the slope of the line and a point on the line, we only have to substitute the appropriate values in the point-slope equation.

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

Normally, we would be finished, but we must change the double negative to a positive to have this in proper form.

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