Question

A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $80, and the club is charging $10 per student that attends.

Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?

graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 80 through the point 2 comma negative 100
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 80 through the point 2 comma negative 60
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 80 through the point 2 comma 60
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 80 through the point 2 comma 100

Answer 1

To represent the middle school club's earnings from a homecoming dance, starting with a $80 cost for decorations and earning $10 per student, the graph should start at (0, -$80) and have a positive slope of 10, indicating an increase of $10 in funds raised for every additional student. The break-even point would be at (8, $0).

Step-by-step explanation:

The scenario of the middle school club raising money for a homecoming dance by charging $10 per student with an initial cost of $80 in decorations can be modeled by a linear equation. Since the club starts with a debt of $80 (cost of decorations), the graph will begin at (0, -$80) on the y-axis (amount of money raised). For every student that attends, the club earns $10, so the slope of the line is positive. The correct graph would show a line where with each additional student, the amount of money raised increases by $10. Therefore, the line would intersect the y-axis at -80 and have a slope of +10. If 8 students attend, the club will break even (8 students x $10 per student = $80), and the point on the graph would be (8, $0). For more than 8 students, the graph would show positive earnings. A graph depicting this would show the line passing through the points (0, -$80) and (8, $0), with the line continuing upwards to the right.