# If a line passes through the points (1, 3) and (0, 0), what is the equation of the line?

##### 1 Answer
May 10, 2017

$y = 3 x$

#### Explanation:

Use the slope formula to first determine the slope:
$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

If we let $\left(1 , 3\right) \to \left(\textcolor{b l u e}{{x}_{1}} , \textcolor{red}{{y}_{1}}\right) \mathmr{and} \left(0 , 0\right) \to \left(\textcolor{b l u e}{{x}_{2}} , \textcolor{red}{{y}_{2}}\right)$ then,

m=(color(red)(0)color(blue)(-3))/(color(red)(0)color(blue)(-1) $= \frac{- 3}{-} 1 = 3$

Now that we know our slope is $3$ we can find the equation of the line by using the slope and any of the two points given into the point-slope formula: $y - {y}_{1} = m \left(x - {x}_{1}\right)$ I will use $\left(0 , 0\right)$

$y - 0 = 3 \left(x - 0\right)$

We then simplify and write in terms of $y = m x + b$

$y = 3 x - 0 \to y = 3 x$

Graphically, the equation looks like this: (You can actually interact with the graph with your mouse and you'll see that the line does in fact go through the points $\left(0 , 0\right)$ and $\left(1 , 3\right)$ graph{3x [-10, 10, -5, 5]}