# How do you write the equation of the line with point (2, 1) with slope 3?

Jul 22, 2016

$y = 3 x - 5$

#### Explanation:

Let $\left(x , y\right)$ be a point on the line. Then the slope of the segment joining it to $\left(2 , 1\right)$ (which, of course, is just the slope of our line) is

$\frac{y - 1}{x - 2}$

Thus we have

$\frac{y - 1}{x - 2} = 3$

This is the equation of the straight line that we want. Rearranging, we can write the equation in the standard form

$y - 1 = 3 \left(x - 2\right)$
or
$y - 1 = 3 x - 6$
or
$y = 3 x - 5$