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Recognizing Points for an Inequality

2.12.5 Recognizing Points for an Inequality

2.12.5 • Recognizing Points for an Inequality

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To raise money for after-school programs at an elementary school, a group of parents is holding a weekend of games in a community center. They charge $8 per person for entry into the event. The group would like to earn at least $600, after paying for the cost of renting the space, which is $40 an hour.

1.

If x x represents the number of entry tickets sold and y y the hours of space rental, which inequality represents the constraints in the situation?

a. 8 x − 40 y < 600 8 x − 40 y < 600

b. 8 x − 40 y ≤ 600 8 x − 40 y ≤ 600

c. 8 x − 40 y > 600 8 x − 40 y > 600

d. 8 x − 40 y ≥ 600 8 x − 40 y ≥ 600

Compare your answer:

d

2.

The line is the graph of 8 x − 40 y = 600 8 x − 40 y = 600 . Select all points whose ( x , y ) ( x , y ) values represent the group reaching its fundraising goal. Be prepared to show your reasoning.

The graph of a line in the first quadrant. The x-axis represents the number of tickets sold and the y-axis represents the hours of space rental. Three points are labeled. Point A is located at (100, 10) in the region above the line. Point B is located at (180, 21) on the line. Point C is located at (200, 5) in the region below the line.

Compare your answer:

Points B and C. Sample explanation: When the coordinates of B and C are substituted for the x x and y y in the equation, they result in a number that is at least 600.

3.

Complete the graph so that it represents solutions to an inequality that represents this situation. (Be clear about whether you want to use a solid or dashed line.) Use the graphing tool or technology outside the course. Graph the equation that represents this scenario using the Desmos tool below.

The graph of a line in the first quadrant. The x-axis represents the number of tickets sold and the y-axis represents the hours of space rental. Three points are labeled. Point A is located at (100, 10) in the region above the line. Point B is located at (180, 21) on the line. Point C is located at (200, 5) in the region below the line.

Compare your answer:

The graph of an inequality in the first quadrant. The x-axis represents the number of tickets sold and the y-axis represents the hours of space rental.
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