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

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

`y=mx+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=2/3(2x-4)`

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

`y=2/3*2x-2/3*4`
`y=(4x)/3-8/3`

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

`m=4/3`
`c=-8/3`

We conclude that the slope of this line is `4` in `3`. It crosses the `y`-axis at a height of `-8/3`, or `-2.6` recurring.