Rowe Floyd
12/23/2023 · Senior High School
Question After school, a group of students decides to have a snowball fight. With 2 students on a team, they can make 6 snowballs per minute. With 10 students on a team, they can make 30 snowballs per minute. What is the slope in this situation? Do not include units in your answer.
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Step-by-step Solution
To find the slope in this situation, we can analyze the relationship between the number of students on a team and the number of snowballs made per minute.
We have two data points based on the information provided:
1. With 2 students, they can make 6 snowballs per minute. This gives us the point (2, 6).
2. With 10 students, they can make 30 snowballs per minute. This gives us the point (10, 30).
The slope (m) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting our points into the formula:
- Let \((x_1, y_1) = (2, 6)\)
- Let \((x_2, y_2) = (10, 30)\)
Now, we can calculate the slope:
\[
m = \frac{30 - 6}{10 - 2} = \frac{24}{8} = 3
\]
Thus, the slope in this situation is \(3\).
Quick Answer
The slope is 3.
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