The cost of one pencil is $3, and the total cost of three pencils is $9. which of the following is true?
a.
the number of pencils and the total cost are in a proportional relationship because the cost does not increase with the number of pencils.
b.
the number of pencils and the total cost are in a proportional relationship because the cost of zero pencils is $0, and each pencil costs $3.
c.
the number of pencils and the total cost are in a proportional relationship because the cost of zero pencils is $0 and it does not increase proportionally with the number of pencils.
d.
the number of pencils and the total cost are in a proportional relationship because the cost increases with the number of pencils.

The number of pencils and the total cost are in a proportional relationship because the cost of zero pencils is $0 and each pencil costs $3.

Step-by-step explanation:

The graph of a proportional relationship is represented by a straight line that passes through the origin, (0,0).

In this case, the cost of zero pencils is $0. So, the graph will include the point (0,0). Also, the cost of pencils increases proportionally with the number of pencils.

Therefore, the number of pencils and the total cost are in a proportional relationship because the cost of zero pencils is $0 and each pencil costs $3.

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step-by-step explanation:

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- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."