Total Sodium in Snack (mg) Sodium in Ben's Snack y 220 200 180 160 140 120 100 80 60 40 20 0 1 2 3 4 5 6 7 8 9 Number of Pretzels x
The Correct Answer and Explanation is:
Correct Answer:
Each pretzel adds 20 mg of sodium to Ben’s snack. The total sodium in the snack is calculated using the linear relationship:Total Sodium (mg)=20x+60\text{Total Sodium (mg)} = 20x + 60Total Sodium (mg)=20x+60
where xxx is the number of pretzels.
Explanation
The graph titled “Sodium in Ben’s Snack” displays a linear relationship between the number of pretzels (x-axis) and the total sodium in the snack (y-axis) measured in milligrams (mg). To understand the pattern and find the rule or equation that governs the graph, we must analyze key points and the nature of the line.
From the graph:
- When x=0x = 0x=0 (no pretzels), the total sodium is 60 mg. This suggests that Ben’s snack contains a base sodium level of 60 mg even without any pretzels—perhaps due to other ingredients.
- When x=1x = 1x=1, the sodium is about 80 mg.
- When x=2x = 2x=2, it’s 100 mg, and so on.
The pattern shows that each additional pretzel adds 20 mg of sodium. This indicates a linear increase in sodium content with each added pretzel.
The slope of the line is 20, meaning the sodium increases by 20 mg per pretzel. The y-intercept is 60, the sodium amount when no pretzels are eaten.
This relationship can be written as a linear equation:y=20x+60y = 20x + 60y=20x+60
Where:
- yyy is the total sodium in milligrams,
- xxx is the number of pretzels,
- 20 is the sodium per pretzel,
- 60 is the base sodium without any pretzels.
This kind of graph helps visualize how ingredients contribute to nutritional content, supporting better food choices. In this case, it shows that pretzels add sodium linearly, which is important for people monitoring salt intake.
