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Imagine you're on a serene river, watching Claudia row with effortless grace. But have you ever wondered about the mathematics behind her strokes? Let's dive into a fascinating rowing exercise that will not only challenge your mathematical prowess but also reveal the beauty of linear equations.
How many strokes can Claudia complete in a given time? That's the question that beckons us. So, pause for a moment and see if you can derive an equation to find the answer.
In a span of 15 minutes, Claudia accomplishes 450 strokes. Intriguing, isn't it? Let's visualize this with a simple table. On one side, we have time in minutes (our X variable), and on the other, we have strokes (our Y variable).
At 15 minutes, we have 450 strokes. But what about when the time is zero? How many strokes would Claudia have completed then? The answer is simple: zero. She hasn't had the chance to row yet.
Now, here's where it gets interesting. As time increases by 15 minutes, the strokes increase by 450. What does this tell us? It tells us about the rate of change, or the slope of our linear equation. To calculate this, we divide the change in strokes by the change in time: 450 strokes divided by 15 minutes equals 30 strokes per minute. This rate, incidentally, is the same as the slope of a line.
So, how do we express this relationship as an equation? It's quite straightforward. The number of strokes (Y) is directly proportional to the time in minutes (X), with a constant rate of 30 strokes per minute (our slope, M). Thus, our equation becomes Y = 30X.
Let's validate this equation. When X is zero, Y should also be zero (since Claudia hasn't rowed yet). And when X is 15 minutes, Y should be 450 strokes, which matches our initial data point. Voilà! Our equation holds true.
In conclusion, the next time you watch Claudia row, remember that behind her fluid movements lies a simple yet elegant mathematical equation that captures her rowing rate. Who knew that rowing could be such a delightful blend of art and science?
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