Question

the graph shows the relationship between the weight of silver and the total cost. which of the following is true?
select all that apply
a. the point (1,17) shows the constant of proportionality.
b. the point (0,0) means that 0 pounds of silver cost $0.00.
c. the graph shows a proportional relationship.
d. the point (2,34) means that 34 pounds of silver cost $2.00 per pound.
e. the point (4,68) means that $4.00 is the cost for 68 pounds of silver

Explanation:

Step1: Check constant of proportionality

For a proportional relationship \(y = kx\), when \(x = 1\), \(y=k\). In the graph, when \(x = 1\) (weight = 1 pound), \(y = 17\) (cost=\(17\)). So \(k = 17\), and the point \((1,17)\) shows the constant of proportionality.

Step2: Analyze \((0,0)\)

When \(x = 0\) (weight of silver \(=0\) pounds), \(y = 0\) (total cost \(=0\)). So the point \((0,0)\) means \(0\) pounds of silver cost \(\$0.00\).

Step3: Check proportional relationship

A proportional relationship has the form \(y=kx\) and passes through the origin \((0,0)\). The given graph is a straight - line passing through \((0,0)\), so it shows a proportional relationship.

Step4: Analyze \((2,34)\)

The point \((2,34)\) means when \(x = 2\) (weight \(=2\) pounds), \(y = 34\) (total cost \(=\$34\)). The cost per pound is \(\frac{y}{x}=\frac{34}{2}=17\) dollars per pound, not \(\$2\) per pound.

Step5: Analyze \((4,68)\)

The point \((4,68)\) means when \(x = 4\) (weight \(=4\) pounds), \(y = 68\) (total cost \(=\$68\)), not that \(\$4\) is the cost for \(68\) pounds of silver.

Answer:

A. The point \((1,17)\) shows the constant of proportionality.
B. The point \((0,0)\) means that \(0\) pounds of silver cost \(\$0.00\).
C. The graph shows a proportional relationship.