Question

ashley is a member of the movie-a-month club, where she rents movies each month. she uses the table below to keep track of the number of movies she rents each month and the total cost, which includes her monthly membership fee.

number of movies vs. total cost
number of movies: 12, 15, 9, 22
total cost: $35.00, $42.50, $27.50, $60.00

ashley graphed the relationship in the table. what is the slope of the graph, and what does it represent?

the slope of the graph is 2.50, and it represents the cost of each movie.
the slope of the graph is 2.50, and it represents the amount of the membership fee.
the slope of the graph is 5, and it represents the cost of each movie.
the slope of the graph is 5, and it represents the cost of the membership fee.

Explanation:

Calculate the slope of the linear relationship

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{42.50 - 35.00}{15 - 12} = \frac{7.50}{3} = 2.50 $$

Interpret the meaning of the slope

$$ \text{Slope} = \frac{\Delta \text{Total Cost (in dollars)}}{\Delta \text{Number of Movies}} = 2.50 \text{ dollars per movie} $$

Identify the correct option

$$ \text{Slope} = 2.50 \implies \text{Cost of each movie} $$

Answer:

• The slope of the graph is 2.50, and it represents the cost of each movie. (Correct answer)
• The slope of the graph is 2.50, and it represents the amount of the membership fee.
• The slope of the graph is 5, and it represents the cost of each movie.
• The slope of the graph is 5, and it represents the cost of the membership fee.