# How do you find the equation of the line that passes through the points (7,3) and (2,5)?

Dec 15, 2016

$y - 3 = - \frac{2}{5} \left(x - 7\right)$ or $y = - \frac{2}{5} x + \frac{29}{5}$

#### Explanation:

To find the line passing through these two points we will use the point-slope formula. However, first we must determine the slope.

The slope can be found by using the formula: color(red)(m = (y_2 = y_1)/(x_2 - x_1)
Where $m$ is the slope and $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ are the two points.

For our problem we can substitute and find the slope as:

$m = \frac{5 - 3}{2 - 7}$

$m = \frac{2}{- 5} = - \frac{2}{5}$

Now we can use the point-slope formula. The point-slope formula states: $\textcolor{red}{\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)}$
Where $m$ is the slope and #(x_1, y_1) is a point the line passes through.

Substituting the slope we calculated and one of the points we were given.

$y - 3 = - \frac{2}{5} \left(x - 7\right)$

or, converting to slope-intercept form:

$y - 3 = - \frac{2}{5} x + \frac{14}{5}$

$y - 3 + 3 = - \frac{2}{5} x + \frac{14}{5} + 3$

$y - 0 = - \frac{2}{5} x + \frac{14}{5} + 3 \left(\frac{5}{5}\right)$

$y = - \frac{2}{5} x + \frac{14}{5} + \frac{15}{5}$

$y = - \frac{2}{5} x + \frac{29}{5}$