Question

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

Explanation:

Step1: Analyze the meaning of (0, 0)

In a cost - weight relationship, when weight $x = 0$, cost $y=0$. So the point $(0,0)$ means 0 pounds of silver cost $0.00$, this statement is true.

Step2: Determine the constant of proportionality

For a proportional relationship $y = kx$, the constant of proportionality $k=\frac{y}{x}$. For the point $(1,17)$, $k = 17$, so the point $(1,17)$ shows the constant of proportionality, this statement is true.

Step3: Analyze the point (4, 68)

The point $(4,68)$ means that 4 pounds of silver cost $68$, not that $4$ is the cost for 68 pounds, so this statement is false.

Step4: Analyze the point (2, 34)

The point $(2,34)$ means that 2 pounds of silver cost $34$, and the cost per pound is $\frac{34}{2}=17$ dollars per pound, not that 34 pounds of silver cost $2$ per pound, so this statement is false.

Step5: Check for proportionality

A graph of a proportional relationship is a straight - line passing through the origin $(0,0)$. Since the given graph is a straight - line passing through the origin, it shows a proportional relationship, this statement is true.

Answer:

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