Question

The lines graphed below dhow the amounts of water in two tanks as they were being filled over time.

For each tank, explain whether or not there is a proportional relationship between the amount of water, in gallons, and the time in minutes. If there is a proportional relationship, identify the unit rate. Use specific features of the graph to support your answer.

Answer 1

There is a proportional relationship. You can tell this because the graph is a straight line.

The unit rate for tank A is 666 2/3 gallons per minute. You will determine this by using the rate 1000 gallons in 1.5 minutes. 1000/1.5 = 666.66... or 666 2/3 gallons.

The unit rate for Tank B is 300 gallons per minute. You can determine this by using 600 gallons in 2 minutes. 600/2 = 300 gallons per minute.

Answer 2

For Tank B there will be a proportional relationship between the time and amount of water.

    Use the fact to get the relationship between two variables of a linear function,

"If a linear function passes through the origin, variables of the function will be proportional".

y = mx + b

If b or y-intercept = 0,

Graph will pass through the origin and the function will be proportional.

From the graph attached,

     Since, straight line is passing through the origin, relationship between time and the amount of water for Tank B shows the proportional relationship.

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