Be careful when shading. Negative numbers of games and snacks do not make sense in this scenario.
Inequality: 0.75x+2.25y ≤ 20 Graph:
Example Solutions: See solution.
Practice makes perfect
Let x represent the number of arcade games played and let y represent the number of snacks purchased. This makes the total cost of games 0.75x and the total cost of snacks 2.25y. These totals, together, cannot exceed $20.
0.75x+2.25y ≤ 20
Now that we have an inequality, we can graph it. To make it easier, we can solve the inequality for y and put it into slope-intercept form.
The inequality is now in slope-intercept form. To graph, we will plot the y-intercept and use the slope to find a second point on the line. Then, we will draw a line through the two points. Since this inequality is less than or equal to, the line will be solid.
All that is left to do is to shade the appropriate region. To decide where to shade, we will pick a test point above or below the line. Then, we will test the point in the inequality. For simplicity, let's try the origin.
Since we have a true statement, the origin is in the region that needs to be shaded, which is below the line.
Note that we do not shade past the x- or y-axes in this case. That would represent negative numbers of games and snacks, respectively, which does not make sense in this scenario.
Interpreting Solutions
As we saw, the origin is a solution to the inequality. It represents not purchasing any snack and not playing any arcade games. This means that no money is spent, which is less than $20. Any other point in the shaded region will also be a solution to the inequality. For example, (1,1), where we play one arcade game and buy one snack.
