Question

hot dog eating contest 1. On the first graph, which point shows Andre's consumption and which shows Jada's consumption? Label them.2. Draw two lines: one through the origin and Andre's point, and one through the origin and Jada's point.3. Write an equation for each line. Use t to represent time in minutes and h to represent number of hot dogs.a. Andre:b. Jada4. For each equation, what does the constant of proportionality tell you?5. Repeat the previous steps for the second graph.

Answer 1

1.

Andre eats 10 hotdogs in 3 minutes.

Jada are 12 hotdogs in 5 minutes.

The first graph shows the number of hotdogs eaten (y-axis) in relation with the time passed (x-axis)

If the points show how many hotdogs they ate in a determined time, since Andre's time (x=3) is less than Jada's (x=5) then the first point represents Andre's information and the second point represents Jada's information.

2. The origin is point (0,0) for the first graph it indicates that at time zero, both Andre and Jada ate no hot dogs.

3.

If "t" represents the variable time, and "h" represents the number of hot dogs.

To determine the equation for each line you have to calculate the constant of proportionality, that is the number of hotdogs they eat per minute

If h and t have a direct relationship then

`h=kt`

Where k is the constant of proportionality, and you can calculate it as

`k=(h)/(t)`

To determine the equations for the lines you have to calculate the constant of proportionality using the time and number of hot dogs provided for Andre and Jada and then replace the value of k in the expression above

a. Andre (3,10)

`k=(h)/(t)=(10)/(3)`

The equation for Andre's line is

`h=(10)/(3)t`

b. Jada (5,12)

`k=(h)/(t)=(12)/(5)`

The equation for Jada's line is

`h=(12)/(5)t`

4. As mentioned before, for these equations the constant of proportionality indicates the number of hot dogs Andre and Jada ate per minute.

5. The second graph shows the relation between the time (y-axis) and the number of hotdogs (x-axis) they ate. From this graph, you can tell how much time it takes Andre and Jada to eat a determined number of hot dogs.

Jada ate more hot dogs than Andre and it took more time, so the lower point represents Andre's information and the second point represents Jada's information

Now that we know which point represents Andre and which represents Jada, you can draw the lines from the origin

For this graph, the variable's positions are inverted, as mentioned before, it represents the relationship of the time vs the number of hotdogs, we can express this relationship as

`t=kh`

For every hot dog eaten k minutes pass. The constant of proportionality indicates the time that it takes to eat a given number of hot dogs.

You can calculate the constant of proportionality as

`k=(t)/(h)`

To determine the equations for the lines you have to calculate the constant of proportionality using the number of hot dogs and time provided for Andre and Jada and then replace the value of k in the expression above

Andre (10,3):

`k=(3)/(10)`

The equation for the line is

`t=(3)/(10)h`

Jada (12,5):

`k=(5)/(12)`

The equation for the line is

`t=(5)/(12)h`

As mentioned before, the content of proportionality indicates the time it takes Andre and Jada to eat one hot dog.