# How do you write the equation of the line that passes through the point (6, -2) and has a slope of -2/3?

Oct 25, 2017

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

#### Explanation:

Given that we have the slope and a point on the graph we can use the point slope formula to find the equation of the line.

Point-Slope Formula: $y - {y}_{1} = m \left(x - {x}_{1}\right)$, where $m$ is the slope of the line and ${x}_{1}$ and ${y}_{1}$ are x and y coordinates of a given point.

We can summarize the information already given:

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

${x}_{1} = 6$

${y}_{1} = - 2$

Using this information, we can substitute these values onto the point-slope formula:

$y - \left(- 2\right) = - \frac{2}{3} \left(x - \left(6\right)\right)$

$y + 2 = - \frac{2}{3} \left(x - 6\right)$

The equation above is the equation of the line in point-slope form. If we wanted to have the equation in $y = m x + b$ form then we simply solve the equation above for $y$

$y + 2 = - \frac{2}{3} x + \frac{12}{3}$

$y \cancel{+ 2 - 2} = - \frac{2}{3} x + \frac{12}{3} - 2$

$y = - \frac{2}{3} x + \frac{12}{3} - 2 \left(\frac{3}{3}\right)$

$y = - \frac{2}{3} x + \frac{12}{3} - \frac{6}{3}$

$y = - \frac{2}{3} x + \frac{6}{3}$

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