A solid line in the xy plane passes through the points (0, -4), (1, -1), and (2, 2). The line divides the plane into two halves. The top half is shaded. A solid line in the xy plane passes through the points (0, -4), (1, -1), and (2, 2). The line divides the plane into two halves. The top half is shaded. If the shaded region in the graph represents the solution set to an inequality, which of the following could be the inequality?

Question

A solid line in the xy plane passes through the points (0, -4), (1, -1), and (2, 2). The line divides the plane into two halves. The top half is shaded.                                           A solid line in the xy plane passes through the points (0, -4), (1, -1), and (2, 2). The line divides the plane into two halves. The top half is shaded. If the shaded region in the graph represents the solution set to an inequality, which of the following could be the inequality?

Bytelearn · Accepted Answer

Calculate Slope: Find the slope of the line passing through the points (0, -4) and (1, -1). The slope (m) is calculated by the change in y divided by the change in x. m = (y2 - y1) / (x2 - x1) m = (-1 - (-4)) / (1 - 0) m = 3 / 1 m = 3Find Equation: Use the slope and one of the points to find the equation of the line in slope-intercept form (y = mx + b). We can use the point (0, -4) and the slope 3 to find b. y = mx + b -4 = 3(0) + b b = -4 The equation of the line is y = 3x - 4.Determine Inequality: Determine the inequality that represents the shaded region above the line. Since the top half of the plane is shaded, we are looking for y values that are greater than the values on the line. The inequality will be y > 3x - 4.

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