# How do you write an equation of a line given (7,-4) and m=2/5?

Mar 15, 2017

See below.

#### Explanation:

This is an example of the use for point-slope form for a line.

Point-slope form shows the relationship between the slope of a line and a point on the line, or mathematically, $y - {y}_{0} = m \left(x - {x}_{0}\right)$, where $\left({x}_{0} , {y}_{0}\right)$ is the point, and $m$ is the slope.

Given that $\left({x}_{0} , {y}_{0}\right) = \left(7 , - 4\right)$, and $m = \frac{2}{5}$, we plug these into the equation.

$y - \left(- 4\right) = \frac{2}{5} \left(x - 7\right)$
$y = \frac{2}{5} \left(x\right) - \frac{14}{5} - 4$

$y = \frac{2}{5} \left(x\right) - \frac{34}{5}$