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?
Clearly, if he plays no games, he scores no goals, so (0,0) is point on the line
the given point is (82,42)
slope = (42-0)/(82-0) = 42/82 = 21/41
(good example of something which makes perfect sense in math,
but makes no sense in reality. Love to see a video of Keith scoring that
1/2 goal )
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 need to use the formula for slope, which is:
slope = (change in y) / (change in x)
In this case, the change in y represents the change in the number of goals, and the change in x represents the change in the number of games.
To calculate the change in y, we subtract the initial number of goals from the final number of goals. In this case, Keith scored 42 goals last season.
Change in y = final number of goals - initial number of goals
Change in y = 42 - 0
Change in y = 42
To calculate the change in x, we subtract the initial number of games from the final number of games. In this case, Keith played 82 games last season.
Change in x = final number of games - initial number of games
Change in x = 82 - 0
Change in x = 82
Now, we can calculate the slope:
slope = (change in y) / (change in x)
slope = 42 / 82
slope = 0.5122
Therefore, the slope of the line that represents the relationship between the number of games and the number of goals scored by Keith is approximately 0.5122.