Step-by-step explanation:
The given inequality is
2x + 8y ≥ 16
To graph the inequality, we first need to graph the line that separates the region, so we need to graph 2x + 8y = 16
To graph the line 2x + 8y = 16, we need to identify two points.
If x = 0
2x + 8y = 16
2(0) + 8y = 16
8y = 16
8y/8 = 16/8
y = 2
If y = 0
2x + 8y = 16
2x + 8(0) = 16
2x = 16
2x/2 = 16/2
x = 8
Therefore, to graph the line, we will use the points (0, 2) and (8, 0)
Then, we need to identify the region, so let's see if the point (x, y) = (0, 0) belongs to the correct region
If (x, y) = (0, 0)
2x + 8y ≥ 16
2(0) + 8(0) ≥ 16
0 ≥ 16
Since 0 is not greater than 16, (0, 0) doesn't belong to the region, and the correct region is above the line 2x + 8y = 16.
Answer:
Now, we can graph the inequality as follows: