Question

What is an equation of the function graphed below

Answer 1

4x-6y=24

Explanation:

Linear equations are typically represented in slope-intercept form:

`y=mx+b`

• m = slope
• b = y-intercept

First, let's find the equation for this graph.

Slope

Slope equation:
`(rise)/(run)`

As shown by the graph, for every 3 squares the line travels right, it travels 2 squares up. Therefore, it has a slope of
`(2)/(3)`. Plug this into
`y=mx+b`:

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

Y-intercept

The graph shows that the line intercepts the y-axis at -4. Plug this into our equation:

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

Rearranging our equation

Now, since the given options do not have the equation written in slope-intercept form, we should rearrange it for easier comparison.

`y=(2)/(3)x-4\\\\3y=2x-12\\\\-2x+3y=-12\\\\2x-3y=12`

Multiply both sides by 2:

`4x-6y=24`

Thus, the equation of the function is
`4x-6y=24`.