Canned Food Drive - Solutions

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MS 51 Canned Food Drive: Variables, Predictions, Graphs, and Linear Equations (y=mx+b)

You are about to drive the Batmobile. But before you can drive, you need to know about the car’s miles per gallon rate. You found out that you can drive 50 miles with 2.4 gallons of gas.

Your task is to:

1. Determine and Identify the Independent Variable and Dependent Variable. Explain your reasoning.

a. Independent Variable:                                          
Gallons of Gas
Explain you reasoning:

The affects the number of miles traveled, so the number of gallons of gas is independent.

b. Dependent Variable:

Miles Traveled

Explain you reasoning:
I am measuring the amount of miles traveled.
The dependent variable is the one we measure.

2. Complete a table for number of hours from zero to ten (in 25 mile intervals).

X: Gallons of Gas	0	1.2	2.4	3.6	4.8	6.0	7.2	8.4	9.6
Y: Miles Traveled	0	25	50	75	100	125	150	175	200

3. Predict the number of gallons needed to drive 500 miles.

If 200 miles need 9.6 gallons, then 400 miles would need twice as much as 9.6., which is 19.2 gallons.

We can keep building and add 100 miles, which is 4.8 gallons. Thus 4.8 plus 19.2 is 24 gallons of gas which is needed to travel 500 miles.

4. What would be the miles traveled if you had 20 gallons of gas?

We can solve this with a proportion:         

20 gallons can let us travel 416.6 miles.

6. What is the Slope of your function?

What does the slope represent?

Rate of change =

Dependent divided by independent = DV/IV = 50/2.4 = 20.83
50miles/2.4gallons = 20.83miles per gallon

m=rate of change=slope=20.83

7. Write a linear equation that represents the number of cans collected per hour. Identify and label what each part of the equation represents in terms of the situation.

Y=20.83x

Y=number of miles

X= number of gallons

M= 20.83 miles per gallon