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Algebra 1

2.12.5 Recognizing Points for an Inequality

Algebra 12.12.5 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 xx represents the number of entry tickets sold and yy the hours of space rental, which inequality represents the constraints in the situation?

a. 8x−40y<6008x−40y<600

b. 8x−40y≤6008x−40y≤600

c. 8x−40y>6008x−40y>600

d. 8x−40y≥6008x−40y≥600

2.

The line is the graph of 8x−40y=6008x−40y=600. Select all points whose (x,y)(x,y) values represent the group reaching its fundraising goal. Be prepared to show your reasoning.

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.

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