Final answer:
To graph the inequalities, plot the line r + y = 5 and the boundary line 8r + 12y = 120, then shade the regions where each inequality is satisfied and find the intersection where both hold true.
Step-by-step explanation:
To graph the inequalities, we start by graphing the line r + y = 5. This line represents the boundary where equality holds true. For values of r and y that satisfy r + y < 5, the points lie below this line.
The second inequality, 8r + 12y ≥ 120, can also be graphed by first finding the boundary line 8r + 12y = 120. To find where the inequality holds true, we need to determine if the region above or below the line satisfies the inequality. We can substitute a point not on the line (for example, the origin (0,0) if the line does not pass through it) into the inequality to check this. Since 8(0) + 12(0) is not greater than 120, the region containing the origin does not satisfy the inequality, which means the area of interest is above the line.
After both boundary lines are plotted, the area of interest (where both inequalities hold true) should be shaded on the graph. It is the intersection of the regions in which each inequality is satisfied.