Question

giancarlo buys granola. the graph shows the relationship between the weight and the cost of the granola. which of the following are true statements about the graph? choose all the correct answers. a the point (8, 24) means that 8 pounds of granola costs $24. b the point (1, 3) means that the rate is $3 per pound of granola. c the point (4, 12) means that it costs $4 for 12 pounds of granola. d since the line passes through (1, 3), 3 is the constant of proportionality. e the graph is not a proportional relationship.

Explanation:

Step1: Analyze point (8, 24)

The point (8, 24) on a cost - weight graph means that when the weight of granola is 8 pounds, the cost is 24 dollars. The unit rate is $\frac{24}{8}=3$ dollars per pound. So statement A is correct.

Step2: Analyze point (1, 3)

The point (1, 3) means that for 1 pound of granola, the cost is 3 dollars, so the rate is 3 dollars per pound. Statement B is correct.

Step3: Analyze point (4, 12)

For the point (4, 12), the unit rate is $\frac{12}{4} = 3$ dollars per pound, not that it costs 4 dollars for 12 pounds. So statement C is incorrect.

Step4: Check line passing through (1, 3)

If a relationship is proportional, the graph is a straight - line passing through the origin $(0,0)$. Just because the line passes through (1, 3) doesn't mean 3 is the constant of proportionality. The constant of proportionality is found by $\frac{y}{x}$ for any non - origin point on the line, and for a proportional relationship, the line must pass through (0,0) which is not clear from the information about just passing through (1, 3). Also, we can see from the graph that it does not pass through the origin, so the relationship is not proportional. Statement D is incorrect and statement E is correct.

Answer:

A. The point (8, 24) means that 8 pounds of granola costs $24.
B. The point (1, 3) means that the rate is $3 per pound of granola.
E. The graph is not a proportional relationship.