Pregunta
\begin{tabular}{l} In her free time, Jackie likes to play an online math game. She noticed that, as she advance \\ to higher levels, her scores generally increased. Jackie tracked her level, \( x \), and score, \( y \), ov \\ several weeks. Then, she calculated a line of best fit. \\ The equation for the line of best fit is \( y=8.1 x+4.5 \). \\ In this context, what does the slope of 8.1 tell you? \\ Jackie started the game with about 8 points. \\ Jackie played about 8 levels of her game. \\ Jackie's score increased about 8 points per level. \\ Jackie's score increased about a point every 8 levels. \\ \hline\end{tabular}
Ask by Floyd Young. in the United States
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The slope of 8.1 means Jackie's score increases by about 8 points per level.
Solución
The equation of the line of best fit is \( y = 8.1x + 4.5 \), where:
- \( y \) represents Jackie's score.
- \( x \) represents the level she reached.
In this linear equation:
- The **slope** (\( 8.1 \)) indicates the rate at which Jackie's score changes with each additional level.
- The **y-intercept** (\( 4.5 \)) suggests Jackie's starting score when \( x = 0 \) (i.e., at the very beginning of the game).
Therefore, the slope of **8.1** means that **for each level Jackie advances, her score increases by approximately 8 points**.
**Answer:**
Jackie’s score increased about 8 points per level.
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Simplifique esta solución Beyond the Answer
The slope of 8.1 in Jackie's equation tells us that for every level she advances in the game, her score increases by approximately 8.1 points. This is a considerable boost, showing that as Jackie progresses, her performance gets significantly better, making it more rewarding and fun! In real-world applications, this concept of slope can be seen in various fields like economics, where it might represent the rate of change of sales with respect to marketing spend. Understanding how different variables are connected helps in making strategic decisions, whether in gaming or business!
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