Question

What is the equation for the graph shown?

Answer 1

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

Explanation:

The rule for graphs is:

`y = mx + c`

Where
`m` is the gradient and
`c` is the y-intercept (where the line crosses the y-axis)

We can work out c by looking at our graph.

Our line crosses the y-axis at (0, 4). So...
`c=4`

To work out our gradient of a straight line (which is what we have)

We use the formula:

`m = (\triangle y)/(\triangle x)`

The triangle
`\triangle` just means the "change in" the coordinates between any two points.

To calculate the change in y, we can pick any two points on our line!

Let's go for (0, 4) and (-6, 0)

To work out the gradient:

`m = (\triangle y)/(\triangle x) = (0 - 4)/(-6 - 0) = (-4)/(-6) = (4)/(6) = (2)/(3)`

Using our formula

`y = mx + c`

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