Chad used the table to show the ratios of the different types of sports game cards that he owns. For every 2 offense cards, he owns 4 defense cards. Which graph represents the proportional relationship between his defense and offense cards?

Question

Chad’s Sports Cards
Card Type
Kicking Team
Offense
Special Teams
Defense
Quantity
1
2
3
4

On a coordinate plane, a graph titled Chad's Cards has offense on the x-axis and Defense on the y-axis. Points (2, 4) and (4, 8) are plotted.

On a coordinate plane, a graph titled Chad's Cards has offense on the x-axis and Defense on the y-axis. Points (2, 4) and (4, 6) are plotted.

On a coordinate plane, a graph titled Chad's Cards has offense on the x-axis and Defense on the y-axis. Points (4, 2) and (8, 4) are plotted.

On a coordinate plane, a graph titled Chad's Cards has offense on the x-axis and Defense on the y-axis. Points (4, 2) and (6, 4) are plotted.

Answer 1

To determine which graph represents the proportional relationship between Chad's defense and offense cards, we can analyze the ratio provided: for every 2 offense cards, Chad owns 4 defense cards. This establishes the ratio of offense to defense as:

• Offense:Defense = 2:4 = 1:2

This means for every 1 offense card, there are 2 defense cards.

Now, let's look at the points given in each graph option:

1. Graph 1: Points (2, 4) and (4, 8)

   • For (2, 4): 2 offense cards -> 4 defense cards (Correct, as 4 = 2*2)
   • For (4, 8): 4 offense cards -> 8 defense cards (Correct, as 8 = 4*2)

2. Graph 2: Points (2, 4) and (4, 6)

   • For (2, 4): 2 offense cards -> 4 defense cards (Correct)
   • For (4, 6): 4 offense cards -> 6 defense cards (Incorrect, as 6 ≠ 4*2)

3. Graph 3: Points (4, 2) and (8, 4)

   • For (4, 2): 4 offense cards -> 2 defense cards (Incorrect, as ratio 4:2 is not valid)
   • For (8, 4): 8 offense cards -> 4 defense cards (Incorrect, as ratio 8:4 is not valid)

4. Graph 4: Points (4, 2) and (6, 4)

   • For (4, 2): 4 offense cards -> 2 defense cards (Incorrect)
   • For (6, 4): 6 offense cards -> 4 defense cards (Incorrect)

Based on the analysis, the graph that correctly represents the proportional relationship between Chad's defense and offense cards is:

Graph 1: Points (2, 4) and (4, 8).