Question

Which linear inequality represents the graph below given the points (-2, 3) and (0, 2)?

A) y < x - 2
B) y > -x + 2
C) y < -x - 2
D) x < -2

Answer 1

The linear inequality that represents the graph given the points (-2, 3) and (0, 2) is y < -x - 2.

Step-by-step explanation:

The linear inequality that represents the graph given the points (-2, 3) and (0, 2) is y < -x - 2.

To find the linear inequality, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. First, calculate the slope of the line using the given points: m = (y2 - y1) / (x2 - x1). Substitute the values into the formula: m = (2 - 3) / (0 - (-2)) = -1 / 2. The slope is -1/2. Since the line has a negative slope and passes through the point (0, 2), which is below the line, the inequality symbol must be less than (<), and the equation becomes y < -x - 2.