Question

Enter an inequality that represents the graph in the box. What is the inequality?

Answer 1

`y<=3x-1`

Explanation:

The equation of the line itself (without worrying about the inequality) can be found by using the slope-intercept form of a line,

`y=mx+b`

where

`m="slope", b=y"-intercept"`

In this case, we can see that the `b=-1` and `m=3`. This gives:

`y=3x-1`

Now to the inequality. The line is solid, not dotted, which indicates the line is part of the solution.

Let's now figure out if we have a greater or lesser sign to put in. We can do that by seeing that the origin, `(0,0)`, is not part of the solution. Let's drop the values into our equation:

`0=3(0)-1`

`0=-1`

We don't want this point to be part of the solution and so we want the inequality to show this relation as False. Which means we have:

`0 <= -1`

and so therefore:

`y<=3x-1`