Question

emily rents bicycles at a park. a graph shows the relationship between the number of hours the bikes are rented (x) and the total co
the points on the graph are as follows: (0,0) (2,40) (4,80) (6,120)
which of the following are true statements about the graph?
choose the three correct answers. (1 point)
a another point on the graph could be (3, 65) meaning 3 hours will cost $65.
b the point (2, 40) means that 2 hours renting the bike cost $40.
c the line will pass through (20, 1) and 1 is the constant of proportionality.
d the unit rate is $20 per 1 hour of renting the bike.
e the graph will show a proportional relationship.

Explanation:

Step1: Analyze option A

The unit rate is calculated as \(\frac{40}{2}=\frac{80}{4}=\frac{120}{6} = 20\) dollars per hour. For \(x = 3\) hours, \(y=20\times3=60
eq65\). So option A is false.

Step2: Analyze option B

In the coordinate \((x,y)\), \(x\) represents the number of hours and \(y\) represents the cost. For the point \((2,40)\), when \(x = 2\) (hours), \(y = 40\) (cost in dollars). So option B is true.

Step3: Analyze option C

The constant of proportionality \(k=\frac{y}{x}\). For \((2,40)\), \(k = 20\). If \(x = 20\), \(y=k\times x=20\times20 = 400
eq1\). So option C is false.

Step4: Analyze option D

The unit rate \(k=\frac{y}{x}\). Using the point \((2,40)\), \(k=\frac{40}{2}=20\) dollars per hour. So option D is true.

Step5: Analyze option E

The general form of a proportional relationship is \(y = kx\). Here \(y = 20x\) (since \(k = 20\)) and the graph passes through the origin \((0,0)\). So option E is true.

Answer:

B. The point \((2, 40)\) means that 2 hours renting the bike cost \(\$40\).
D. The unit rate is \(\$20\) per 1 hour of renting the bike.
E. The graph will show a proportional relationship.