Question

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 1) and (0, 1). Everything to the left of the line is shaded. Which linear inequality is represented by the graph? y > 2x + 2 y ≥ One-halfx + 1 y > 2x + 1 y ≥ One-halfx + 2

Answer 1

The linear inequality represented by the graph is y > 2x + 2.

Step-by-step explanation:

The linear inequality represented by the graph is y > 2x + 2.

To determine the inequality, we can first find the slope of the line by using the formula:
slope = (change in y)/(change in x)

Using the given points (-1, -1) and (0, 1), the change in y is 1 - (-1) = 2 and the change in x is 0 - (-1) = 1. So, the slope is 2/1 = 2.

Since the slope is positive, the line moves up the y-axis as the x-value increases. Therefore, the shade is above the line, which can be represented by the inequality y > 2x + 2.

Answer 2

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Answer:

(c) y > 2x + 1

Step-by-step explanation:

The line has a rise of 2 for a run of 1, so a slope of 2. Its y-intercept is 1, so the equation of the line is ...

m = rise/run = 2/1 = 2; b = 1

y = mx +b . . . . . . slope-intercept form

y = 2x +1

The shading is above the line, and does not include the line, so the graph is of ...

y > 2x +1