Question

which statements are correct interpretations of this graph? select each correct answer. there are 1.5 g of dietary fiber per tomato. there are 3 g of dietary fiber in every 2 tomatoes. there are 2 g of dietary fiber in every 3 tomatoes. there are 0.7 g of dietary fiber per tomato.

Explanation:

Step1: Calculate the unit rate

The graph passes through the point \((2,3)\). The unit rate \(r\) (grams of dietary fiber per tomato) is calculated as \(r=\frac{y}{x}\), where \(y = 3\) (grams of dietary fiber) and \(x = 2\) (number of tomatoes). So \(r=\frac{3}{2}=1.5\) g per tomato.

Step2: Check each statement

• For the statement “There are \(1.5\) g of dietary fiber per tomato”:

Since the unit rate \(r = 1.5\) g per tomato (from Step 1), this statement is correct.

• For the statement “There are \(3\) g of dietary fiber in every \(2\) tomatoes”:

When \(x = 2\) (number of tomatoes), from the point \((2,3)\) on the graph, \(y=3\) (grams of dietary fiber). So this statement is correct.

• For the statement “There are \(2\) g of dietary fiber in every \(3\) tomatoes”:

Using the unit rate \(r = 1.5\) g per tomato, for \(x = 3\) tomatoes, \(y=r\times x=1.5\times3 = 4.5
eq2\). So this statement is incorrect.

• For the statement “There are \(0.7\) g of dietary fiber per tomato”:

Since \(r = 1.5
eq0.7\), this statement is incorrect.

Answer:

• There are \(1.5\) g of dietary fiber per tomato.
• There are \(3\) g of dietary fiber in every \(2\) tomatoes.