Graph this inequality:

Question

y>–5/6x–4
Plot points on the boundary line. Select the line to switch between solid and dotted. Select a region to shade it.

Answer 1

To graph the inequality y > -(5/6)x - 4, we first need to graph the boundary line y = -(5/6)x - 4.

To find points on the line, we can choose x-values and solve for the corresponding y-values.

Let's choose three x-values: -6, 0, and 6.

When x = -6:
y = -(5/6)(-6) - 4
y = 5 + 4
y = 9

So, one point on the line is (-6, 9).

When x = 0:
y = -(5/6)(0) - 4
y = -4

So, the next point is (0, -4).

When x = 6:
y = -(5/6)(6) - 4
y = -5 - 4
y = -9

So, the third point is (6, -9).

Plotting these points and connecting them, we get a boundary line as shown below:

The line passes through the points (-6, 9), (0, -4), and (6, -9).

However, the inequality is y > -(5/6)x - 4, which means y is greater than the line, not equal to it. Hence, the line should be dotted.

Now we need to shade the region above the line to represent y > -(5/6)x - 4. Since y is greater than the line, any point in the shaded region will satisfy the inequality.

Here is the graph of the inequality y > -(5/6)x - 4:
[Please note that the graph will be provided in textual format, and it may be distorted due to the limitations of text-based responses.]

```
|
y |
↑ |
| /
| /
| _'
-3 -2 -1 0 1 2 3 4 5 6
```

The shaded region will be above the dotted line y = -(5/6)x - 4.