Keith is the leading goal scorer for a team in an ice hockey league. Last season, he scored 42 goals in 82 games. Assuming he scores goals at a constant rate, what is the slope of the line that represents this relationship if the number of games is along the x-axis and the number of goals is along the y-axis?
 A. 21/41
 B. 22/41
 C. 42/23
 D. 41/21


To find the slope of the line that represents the relationship between the number of games and the number of goals scored by Keith, we use the formula for the slope \( m \) of a line, which is the ratio of the change in the y-coordinate to the change in the x-coordinate:

\[
m = \frac{\Delta y}{\Delta x}
\]

In this context:
- \(\Delta y\) (change in goals) = 42 goals
- \(\Delta x\) (change in games) = 82 games

Thus, the slope \( m \) is:

\[
m = \frac{42 \text{ goals}}{82 \text{ games}}
\]

We can simplify this fraction by finding the greatest common divisor (GCD) of 42 and 82. The GCD of 42 and 82 is 2.

\[
m = \frac{42 \div 2}{82 \div 2} = \frac{21}{41}
\]

Therefore, the slope of the line that represents this relationship is:

\[
\boxed{\frac{21}{41}}
\]

Do you want details or have any questions?

Here are 5 questions you can ask next:
1. How do you find the GCD of two numbers?
2. What is the significance of the slope in a linear relationship?
3. How can you interpret the slope in real-world scenarios?
4. What other examples of slopes can be found in sports statistics?
5. How do you graph a linear relationship given a set of data points?

**Tip:** When calculating the slope of a line, always simplify the fraction to its lowest terms to ensure clarity and accuracy.

Learn how to calculate the slope of a linear relationship using Keith's hockey goals example. Understand the concept of rates and linear equations. Suitable for students in Grades 7-9.

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