# How do you graph the linear function f(x)=2/3x+1?

May 9, 2017

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

We need to know three things to graph a linear equation: $x$-intercept, $y$-intercept, and slope.

We can tell, thanks to $y = \textcolor{red}{m} x + \textcolor{\mathmr{and} a n \ge}{b}$, that the $\textcolor{red}{s l o p e}$ is $\textcolor{red}{\frac{2}{3}}$ and the $\textcolor{\mathmr{and} a n \ge}{y - i n t e r c e p t}$ is $\textcolor{\mathmr{and} a n \ge}{1}$. We have two out of the three required pieces of information, but we still need the $x -$intercept.

To find the $x$-intercept, we need to set $y$ equal to zero and solve for $x$:

$0 = \frac{2}{3} x + 1$

subtract $1$ on both sides

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

multiply by $\frac{3}{2}$ on both sides

$\frac{3}{2} \cdot - \frac{1}{1} = \frac{\cancel{3}}{\cancel{2}} \cdot \frac{\cancel{2}}{\cancel{3}} x$

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

So, the $x$-intercept is $\left(- \frac{3}{2} , 0\right)$, the $y$-intercept is $\left(0 , 1\right)$, and the slope is $\frac{2}{3}$. That means we begin at $\left(0 , 1\right)$, and go up $2$, over $3$, and also down $2$, over $3$. We keep doing that forever (that's the nature of a line), and if everything is correct, the line should pass through the point $\left(- \frac{3}{2} , 0\right)$.

Let's check our work
graph{y=2/3x+1}