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? 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 point \((0,0)\)

In a cost - weight relationship, when the weight \(x = 0\) (pounds of silver), the cost \(y=0\) (dollars). So, the statement “The point \((0, 0)\) means that \(0\) pounds of silver cost \(\$0.00\)” is True.

Step2: Analyze the point \((1,17)\)

The constant of proportionality \(k\) in a proportional relationship \(y = kx\) is found by \(k=\frac{y}{x}\). For the point \((x = 1,y = 17)\), \(k=\frac{17}{1}=17\). So, the statement “The point \((1, 17)\) shows the constant of proportionality” is True.

Step3: Analyze the point \((4,68)\)

In the ordered pair \((x,y)\), \(x\) represents the weight (in pounds) and \(y\) represents the cost (in dollars). For the point \((4,68)\), \(x = 4\) (pounds of silver) and \(y = 68\) (dollars). So, the statement “The point \((4, 68)\) means that \(\$4.00\) is the cost for \(68\) pounds of silver” is False.

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

For the point \((2,34)\), using the formula \(y=kx\), if \(x = 2\) and \(y = 34\), then \(k=\frac{y}{x}=\frac{34}{2}=17\). The cost per pound is \(\$17\), not \(\$2\). So, the statement “The point \((2, 34)\) means that \(34\) pounds of silver cost \(\$2.00\) per pound” is False.

Step5: Analyze the graph for proportionality

A proportional relationship has the form \(y = kx\) and its graph is a straight - line passing through the origin \((0,0)\). Since the given graph is a straight - line passing through \((0,0)\), the statement “The graph shows a proportional relationship” 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.