Question

(Graphing Linear Equations MC)

A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $120, 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 120 through the point 2 comma 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 120 through the point 2 comma 140
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 120 through the point 2 comma negative 140
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 120 through the point 2 comma negative 100

Answer 1

"going from the point 0 comma negative 120 through the point 2 comma negative 100"

Explanation:

Let y be the total income from the homecoming dance, and x the number of students who purchase tickets (at $10 each). We are told that it costs $120 for the decorations.

The income from ticket sales would be:

1) the number of tickets sold times $10/ticket, or $10

2) Less the expenses of decorating (-$120)

We can write the total income as:

y = $10x - $120

The graph of this function would be a straight line that has a y-intercept of -$120. Before any ticket is sold, the cost of decorations must be considered. If no tickets are sold (x=0), the total income is -$120.

Using the equation, we can calculate the income when 2 tickets are sold (x=2):

y = $10x - $120

y = $10*(2) - $120 [two tickets sold]

y = -$100

Summary

y = $10x - $120

(0,-$120)

(2,-$100)

This matches the statement "going from the point 0 comma negative 120 through the point 2 comma negative 100" provided in the answer options.

See the attached graph.