Graph this inequality:
y>1/3x+4
Plot points on the boundary line. Select the line to switch between solid and dotted. Select a region to shade it.
To graph the inequality y > (1/3)x + 4, we first need to graph the boundary line y = (1/3)x + 4.
To graph a line, we typically need two points. However, since this is a linear equation in slope-intercept form (y = mx + b), we can use the y-intercept (0,4) and the slope (1/3) to graph the line.
1. Plot the y-intercept at (0, 4).
2. Use the slope (rise over run) of 1/3. From the y-intercept, move up one unit, then move to the right three units. Mark this point as (3, 5).
3. Draw a straight line passing through the two plotted points.
The graphed line should look like this:
```plaintext
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Now, to determine which region to shade, we need to test a point that is not on the line. The easiest point to test is the origin (0, 0).
Substituting these coordinates into the inequality, we get:
0 > (1/3)(0) + 4
0 > 0 + 4
0 > 4
Since 0 is NOT greater than 4, the region that does not include the origin (0, 0) should be shaded.
The graphed inequality (shaded region above the line) should look like this:
```plaintext
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```
Note: The line should be represented as a solid line to indicate that it is included in the solution.