Answer:
A) y ≥ -3x + 4
Step-by-step explanation:
Given the graph of an inequality, where it shows that the y-intercept is (0, 4), and the line has a negative slope (as it declines from left to right). To figure out the value of the slope, choose two points from the graph, and substitute its values into the slope equation,
m = (y2 - y1)/(x2 - x1)
Let (x1, y1) = (0, 4)
(x2, y2) = (2, -2)
m = (-2 - 4)/(2 - 0)
m = -6/2
m = -3
Now that we have the value of the slope, m = -3, and the y-intercept, b = 4:
We need to determine which part of the region is shaded. Choose a test point that is not on the graph. Let's use the point of origin, (0, 0) to see whether it is included as a solution:
Option A: y ≥ -3x + 4
Substitute values of (0, 0) into the inequality statement:
0 ≥ -3(0) + 4
0 ≥ 0 + 4
0 ≥ 4 (False statement). The shaded region must not contain the given test point, (0, 0), which is actually the case in your given graph. The right-half plane is the shaded region. Hence, y ≥ -3x + 4 is the correct inequality statement that represents the graph.
The answer cannot be y ≤ -3x + 4 because if you plug in the test point into y ≤ -3x + 4, it will provide a true statement.
y ≤ -3x + 4
0 ≤ -3(0) + 4
0 ≤ 0 + 4
0 ≤ 4 (True statement, which means that the region where the test point is located should be shaded).
Therefore, the correct answer is Option A) y ≥ -3x + 4
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