# How do you find the equation of a line with a slope of 2 and a y intercept of (0,0)?

Dec 31, 2016

Use slope-intercept form. See below.

#### Explanation:

Slope-intercept form is given by $y = m x + b$, where $m$ is the slope of the line and $b$ is the $y$-intercept of the line, or the value of $y$ where the line crosses the $y$-axis.

Given that the slope of the line is $2$, we have $m = 2$, and because the line crosses the $y$-axis at the point $\left(0 , 0\right)$, where $y = 0$ and $x - 0$, we have:

$y = 2 x + 0$

Or, equivalently, $y = 2 x$

If the point given were not the origin, you could use $y = m x + b$ to find $b$ by plugging the $x$ and $y$ value of the point in for $x$ and $y$ in the equation along with the given slope $m$ and solving for $b$.

Given $m = 2$ and $\left(x , y\right) = \left(0 , 0\right)$:

$0 = 2 \left(0\right) + b$

$\implies 0 = b$

We would then put this value back into $y = m x + b$ for $b$, along with the slope $m$, yielding the same answer as above: $y = 2 x$.