match the graph with its inequality.\na. $y < - 3$\nb. $xgeq2$\nc. $5x + 10y>0$\nd. $y < x$\ne. $2y…

Explanation:

Step1: Find the boundary - line equation

The boundary - line of the given graph is a straight line passing through the points ((0, - 1)) and ((1,2)). The slope (m) of the line using the formula (m=\frac{y_2 - y_1}{x_2 - x_1}) is (m=\frac{2+1}{1 - 0}=3). Using the slope - intercept form (y = mx + b) with the point ((0,-1)), the equation of the boundary - line is (y = 3x-1).

Step2: Determine the inequality sign

The line is solid, so the inequality is either (\leq) or (\geq). The shaded region is below the line, so the inequality is (y\leq3x - 1), which is equivalent to (3x-1\geq y).

Answer:

j. (3x - 1\geq y)