Let's make a graph to see the inequality visually. We can use the x and y-intercepts from the function, 8x + 10y \(\small\mathsf{ \geq }\) 800, to help graph the function. The inequality symbol tells us whether the line will be dotted or solid and whether to shade above or below the line.
To get started, click on the questions below to reveal the answers:
| What is the x-intercept? In other words, at least how many pools must be cleaned if no lawns are mowed (when y = 0, what is x?) | What is the y-intercept? In other words, at least how many lawns must be mowed if no pools are cleaned? |
| The x-intercept is the number of pools that must be cleaned if no lawns are mowed. It is (100,0). | The y-intercept is the number of lawns that must be mowed if no pools are cleaned. It is (0,80). |
Now, graph the function using the points (100,0) and (0,80). Click on the button below to reveal the graph:
You may notice that the inequality is a bit different than other line graphs.
First: Notice that the line is SOLID. In an equality, this tells us the inequality symbol has an equal sign. In this case, the equation is 8x + 10y \(\small\mathsf{ \geq }\) 800. If the equation were 8x + 10y > 800, then the line would be DOTTED.
Next: The coordinate plane is shaded ABOVE the line because the equation is 8x + 10y is greater than or equal to 800. If the equation were 8x + 10y less than or equal to 800, then we would shade BELOW the line.
