# How do you write equation of a line goes through (3,1), with slope of m=1/3?

Jan 28, 2017

Use point-slope form $y - {y}_{1} = m \left(x - {x}_{1}\right)$

#### Explanation:

For this equation that would turn into $y - 1 = \frac{1}{3} \left(x - 3\right)$ then solve which should look like $y = \frac{1}{3} x$

Jan 28, 2017

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

#### Explanation:

You know the equation of a line: $y = m x + b$

You are given the point $\left(3 , 1\right)$. That is the same as saying that $x = 3$ and $y = 1$.

You are given the slope, $m = \frac{1}{3}$. That means that after you "rise" one point on the $y$-axis, you must "run" 3 points on the $x$-axis to get to another point on that line.

Plugging the $x = 3$, $y = 1$, and $m = \frac{1}{3}$ into the equation of a line, you get the following:

$y = m x + b$ becomes $1 = 3 \cdot \frac{1}{3} + b$. The only variable you don't know yet is $b$. So solve for $b$.

$1 = 3 \cdot \frac{1}{3} + b$
$1 = 1 + b$
$b = 0$

The final step is to plug just the slope, $m$ (previously given), and the $y$-intercept, $b$ (which you just found), into the formula $y = m x + b$, giving you:

$y = \frac{1}{3} \cdot x + 0$ or simply $y = \frac{1}{3} \cdot x$