# How do you graph the function y=-2/3x+4?

Jan 23, 2017

There are several strategies you can use to approach this, but since the given equation is in slope-intercept form, let's take advantage of that.

When the equation of a line is given in the form of
$y = \textcolor{p u r p \le}{m} x + \textcolor{b l u e}{b}$, then

$\textcolor{p u r p \le}{m} =$ the slope of the line $\left(\textcolor{p u r p \le}{m} = \frac{\Delta y}{\Delta x}\right)$ and
$\textcolor{b l u e}{b} =$ the y-intercept or where the line crosses the $y$-axis

Since we know that $\textcolor{b l u e}{b} = 4$, we know the line crosses the $y$-axis at $y = 4$. In other words, the line passes through the point $\left(0 , 4\right)$.

Then, applying the slope to that point, we can find a second point on the line.

$\textcolor{p u r p \le}{m} = \frac{\Delta y}{\Delta x} = - \frac{2}{3} = \frac{- 2}{3} = \frac{2}{-} 3$

This tells us that when $x$ changes by $3$ units ($\Delta x$), $y$ changes by $- 2$ units ($\Delta y$)

Starting at $\left(0 , 4\right)$, we can apply the slope:

$\Delta x = 3 = {x}_{2} - 0 \implies {x}_{2} = 3$
$\Delta y = - 2 = {y}_{2} - 4 \implies {y}_{2} = 2$

The point $\left(3 , 2\right)$ will be on the line. Plotting these two points $\left(0 , 4\right)$ and $\left(3 , 2\right)$ and drawing a straight line through these points will give you the graph of the function $y = - \frac{2}{3} + 4$