Answer:
Explanation:
he linear inequality represented by the graph is y > 3x + 2.
To determine the correct inequality, we need to consider the slope and the shading of the graph.
Given that the line has a positive slope and is dashed, we know that it represents an inequality with a greater than or less than symbol. The positive slope indicates that the line slants upward from left to right.
To find the specific inequality, we can compare the slope of the line to the coefficients of x and y in the answer choices.
Let's consider the points (0, 2) and (-3, -7) that the line passes through. We can find the slope of the line using the formula:
slope = (change in y) / (change in x)
For the given points, the change in y is 2 - (-7) = 9, and the change in x is 0 - (-3) = 3.
So the slope of the line is 9/3 = 3.
Now we can compare the slope of the line to the coefficients of x and y in the answer choices.
Looking at the first answer choice, y < 3x + 2, we see that the coefficient of y is 1, which is less than the slope of the line (3). Therefore, this answer choice is incorrect.
The second answer choice, y > 3x + 2, has a coefficient of y that is greater than the slope of the line. Therefore, this answer choice is correct.
The third and fourth answer choices, y < (1/3)x + 2 and y > (1/3)x + 2, have a coefficient of y that is less than the slope of the line. Therefore, these answer choices are incorrect.
In conclusion, the linear inequality represented by the graph is y > 3x + 2. This means that all the points above the dashed line are solutions to the inequality, while the shaded region represents all the points that satisfy the inequality.