Analyzing Inequality Graphs

The Department of Local Renewal is trying to balance what it can reasonably accomplish between time spent on planning (x) and time spent on labor (y) using the graph. The x-intercept for this graph is​ (a)   , while the y-intercept for the graph is ​ (b)   .

They want to be able to model the relationship between the number of people it takes to reasonably accomplish a task if there is only 12 hours of time available in a week. The correct equation for this inequality is​ (a)  

They want to be able to model the relationship between the number of people it takes to reasonably accomplish a task if there is only 12 hours of time available in a week. The values 2 and 3 in the inequality $$2x+3y\le12$$ represent​ (a)  

Someone logged volunteer hours, but didn't include what activity the volunteers were working on. Each activity is mapped by a given inequality. Match the activity inequality to its volunteer hours solution.

The Paths and Travel Subcommittee is trying to determine which side of a path needs sprinklers installed, while not on site. They know they are looking for the inequality that represents the region above the line $$y = -x + 4$$ ?

The committee is interested in modeling the area for a community garden allotment. The feasible region is bounded by the inequalities $$x \geq 0$$ , $$y \geq 0$$ , and $$x + y \leq 6$$ , which point(s) are in the feasible region?

Which of the following models the situation "we need at least 10 volunteers to split between cleaning up the vacant lot and picking up materials"?

If we are trying to learn how much money will be left in the budget at the end of the month, we can use $$x+y<8000$$ as a model. How would we describe the feasible region of this inequality?

This line separates a residential zone from a manufacturing zone. Click on the graph for the side you should shade if the residential zone is modeled by the inequality $$2x-y\le6$$

We are determining the amount of wood we will need to build a given number of benches. If the amount of pallets we need is modeled by the inequality $$y \leq 2x + 1$$ , what would not be a viable point for pallets and benches?