Question

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 3) and (3, 1). Everything below and to the right of the line is shaded.

Which linear inequality is represented by the graph?

y > Two-thirdsx – 2
y < Two-thirdsx + 2
y > Two-thirdsx + 1
y < Two-thirdsx – 1

Answer 1

The linear inequality represented by the graph is y > Two-thirdsx - 2. To determine the correct linear inequality, we need to find the slope of the dashed line using the given points and use that information to form the inequality.

Step-by-step explanation:

The linear inequality represented by the graph is y > Two-thirdsx - 2.

To determine the correct linear inequality, we first need to find the slope of the dashed line using the given points. The slope is found using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the values, we have: m = (1 - (-3)) / (3 - (-3)) = 4 / 6 = 2 / 3.

Since the line has a positive slope, we know that y should be greater than the equation of the line. Hence, the correct linear inequality is y > Two-thirdsx - 2.