Question

9 eva buys walnuts. the graph shows the relationship between the number of scoops and the cost of the walnuts. which of the following are true statements about the graph? choose all the correct answers.
a the point (2, 4) means that 2 scoops of walnuts cost $4.
b since the line passes through (1, 2), 1 is the constant of proportionality.
c the graph is a proportional relationship.
d the point (1, 2) means that the unit rate is $2 per scoop of walnuts.
e the point (3, 6) means that it costs $3 for 6 scoops of walnuts.

Explanation:

Step1: Analyze Option A

The x - axis represents scoops and y - axis represents cost. For the point \((2,4)\), \(x = 2\) (scoops) and \(y=4\) (cost). So 2 scoops cost \$4. This statement is true.

Step2: Analyze Option B

The constant of proportionality \(k=\frac{y}{x}\). For the point \((1,2)\), \(k = \frac{2}{1}=2\), not 1. So this statement is false.

Step3: Analyze Option C

The graph is a straight line passing through the origin \((0,0)\), so it represents a proportional relationship (\(y = kx\) where \(k\) is constant). This statement is true.

Step4: Analyze Option D

For the point \((1,2)\), the unit rate (cost per scoop) is \(\frac{y}{x}=\frac{2}{1} = 2\) dollars per scoop. This statement is true.

Step5: Analyze Option E

For the point \((3,6)\), \(x = 3\) (scoops) and \(y = 6\) (cost), which means 3 scoops cost \$6, not 6 scoops cost \$3. This statement is false.

Answer:

A. The point \((2, 4)\) means that 2 scoops of walnuts cost \$4.
C. The graph is a proportional relationship.
D. The point \((1, 2)\) means that the unit rate is \$2 per scoop of walnuts.