Question

isla kept track of the number of hours and number of laps she swam each week over a six month period.
the scatter plot shows her results.
estimate the line of best fit, and use the line to fill in the drop - downs.
for each increase of 1 dropdown, the average dropdown increases by about dropdown.

Explanation:

Step1: Identify Variables

The x - axis is "Time (hours)" and the y - axis is "Number of Laps". So we are looking at the relationship between time (in hours) and number of laps.

Step2: Analyze the Line of Best Fit

To find the slope (rate of change), we can pick two points on the line of best fit. Let's assume two points, for example, when \(x = 1\) (1 hour), let's say the number of laps \(y\approx30\), and when \(x = 2\), \(y\approx60\) (this is a rough estimate from the scatter plot trend). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). If we take two points like \((1, 30)\) and \((2, 60)\), the slope \(m=\frac{60 - 30}{2 - 1}=30\). But a more accurate estimate from the scatter plot: looking at the general trend, as time (hours) increases by 1, the number of laps increases. Let's take two points that are more representative. For example, when \(x = 5\), the number of laps is around 120, and when \(x = 10\), the number of laps is around 270. The slope \(m=\frac{270 - 120}{10 - 5}=\frac{150}{5} = 30\). So for each increase of 1 in "hour (time)", the average "number of laps" increases by about 30.

Answer:

For each increase of 1 \(\boldsymbol{\text{hour (time)}}\), the average \(\boldsymbol{\text{number of laps}}\) increases by about \(\boldsymbol{30}\).