Question

Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the graph of the following: y < 1/3x + 4

Answer 1

The origin is included in the shaded region and the shaded region is below the line.

Step-by-step explanation:

First, let's graph the line that separates the region: y = 1/3 x + 4

So, to graph the line, we need to find two points in the line as follows:

If x = 0, then y is equal to:

y = 1/3 (0) + 4

y = 4

If x = 3, then y is equal to:

y = 1/3 (3) + 4

y = 1 + 4

y = 5

So, using the points (0, 4) and (3, 5), we get:

Now, we can determine whether the origin is included or not replacing x and y by the coordinates of the origin (0, 0) and determine if this point satisfies the inequality. So:

y < 1/3x + 4​

0 < 1/3(0) + 4

0 < 0 + 4

0 < 4

Since 0 is less than 4, the origin is included in the shaded region, so the shaded region is below the line.