Question

What is the equation of the following graph?

Answer 1

`y <=3x - 1`

Explanation:

First of all, we see that the line is filled (it isn't dotted), so we know we will have the `<= or >=` signs.

Now we find the equation of the line. There is a slope of `3` and a y-intercept at `y = -1`, so the equation is `y = 3x - 1`. We know the origin is not in the solution set, and `3(0) - 1 = -1`, so the inequality will be

`y <= 3x - 1`

It makes sense, because the shaded region is below the line, so the inequality will be `y <= 3x - 1` instead of `y >=3x - 1`.

Hopefully this helps!

Answer 2

`y <= 3x -1`

Explanation:

The line is solid and the area below is shaded, therefore, the inequality is `<=`.

The line of equality passes through the points `(1,2)` and `(0,-1)`. The second point just happens to be the y intercept, therefore, we can use the slope intercept form of the equation of a line:

`y = mx + b`

And we know that b is `-1`:

`y = mx -1`

The slope is:

`m = (2 - -1)/(1-0)`

`m = 3`

The equation of the line is:

`y = 3x -1`

Make the `=` become `<=`:

`y <= 3x -1`