which number completes the system of linear inequalities represented by the graph? y ≥ 2x - 2 and x + 4y ≥…

which number completes the system of linear inequalities represented by the graph? y ≥ 2x - 2 and x + 4y ≥ -12 -3 4 6

which number completes the system of linear inequalities represented by the graph? y ≥ 2x - 2 and x + 4y ≥ -12 -3 4 6

Answer

Explanation:

Step1: Find the x - intercept of the blue line

The equation of the blue line is in the form (x + 4y\geq k). The x - intercept is the point where (y = 0). From the graph, the x - intercept of the blue line is at (x=- 12). Substitute (x=-12) and (y = 0) into the inequality (x + 4y\geq k).

Step2: Calculate the value of k

When (x=-12) and (y = 0), we have (-12+4\times0\geq k). So (k=-12) makes the inequality (x + 4y\geq k) consistent with the graph.

Answer:

-12