# How do you find the slope and intercept of y=2/3(2x-4)?

Jan 9, 2016

Expand the bracket and then compare to the general equation for a straight line, $y = m x + c$.

#### Explanation:

The equation shown describes a straight line. For any straight line, we can write an equation with the form:

$y = m x + c$

What does this mean? The letters $y$ and $x$ are the variables, as usual. The letter $m$ refers to the slope of the line - how steep it is. If this number is positive, the line slopes up to the right. If it's negative, the line slopes down. Finally, the letter $c$ tells us where the line crosses the $y$-axis. It is called the $y$-intercept.

Let's look more closely at the equation provided.

$y = \frac{2}{3} \left(2 x - 4\right)$

Here we have a bracket containing two terms ($2 x$ and $- 4$), which is all multiplied by $\frac{2}{3}$. This is not in the $m x + c$ form that we want! So let's expand the bracket and see what we get:

$y = \frac{2}{3} \cdot 2 x - \frac{2}{3} \cdot 4$
$y = \frac{4 x}{3} - \frac{8}{3}$

Now compare this to the general equation for a straight line, $y = m x + c$. You can see that $m = \frac{4}{3}$ since that's what the $x$ is being multiplied by. The term without $x$ in it is our $y$-intercept, $c$.

$m = \frac{4}{3}$
$c = - \frac{8}{3}$

We conclude that the slope of this line is $4$ in $3$. It crosses the $y$-axis at a height of $- \frac{8}{3}$, or $- 2.6$ recurring.