Question

lamar goes for a bike ride every day. for the last two weeks, he tracked the distance he rode and his time. he made a scatter plot to show the relationship between the distance and time for each of his bike rides. bike rides scatter plot (omitted) which of the following is the best estimate for how long it would take lamar to ride 15 miles?

Explanation:

Step1: Analyze the scatter plot trend

The scatter plot shows a positive linear relationship between distance (x - axis, miles) and time (y - axis, minutes). As distance increases, time generally increases.

Step2: Estimate the time for 15 miles

Looking at the plot, when distance is around 10 miles, time is around 30 - 35 minutes, and when distance is 20 miles, time is around 50 minutes. The relationship seems roughly linear. We can estimate the time for 15 miles by looking at the trend. The mid - point between 10 and 20 miles (15 miles) should have a time that is roughly the mid - point between the times at 10 and 20 miles. At 10 miles, let's take an average of the points around 10 miles, say around 32 minutes. At 20 miles, around 50 minutes. The difference in distance is \(20 - 10=10\) miles, and the difference in time is \(50 - 32 = 18\) minutes. For 5 more miles (from 10 to 15), the time increase would be about \(\frac{18}{2}=9\) minutes. So \(32 + 9=41\) minutes. Alternatively, by visually inspecting the trend line (if we imagine a line of best fit), at \(x = 15\) (15 miles), the \(y\) - value (time) is approximately 40 - 45 minutes. A reasonable estimate is around 40 - 45 minutes, and a common estimate from the trend would be about 40 minutes (or a value in that range).

Answer:

Approximately 40 minutes (or a value in the range of 35 - 45 minutes, depending on the trend estimation. A more precise visual estimate from the scatter plot's trend line would suggest around 40 minutes as a best estimate).