Question

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Explanation:

Identify key data points

We locate representative points along the trend of the scatter plot.
At \(1.5\) hours of study time, the scores are clustered around \(65\) to \(70\).
At \(3.5\) hours of study time, the scores are clustered around \(95\) to \(100\).

Select two representative points

We choose two points to estimate the line of best fit:
Point 1: \((1.5, 68)\)
Point 2: \((3.5, 96)\)

Calculate the estimated slope

We apply the slope formula:

$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$

Substituting our chosen points:

$$ m = \frac{96 - 68}{3.5 - 1.5} = \frac{28}{2} = 14 $$

Verify with alternative points

Using another pair of points along the trend:
Point A: \((1.0, 60)\) (extrapolated trend line start)
Point B: \((3.0, 90)\)

$$ m = \frac{90 - 60}{3.0 - 1.0} = \frac{30}{2} = 15 $$

The estimated slope is approximately \(14\) to \(15\) score points per hour of study.

Answer:

The estimated slope of the line of best fit is approximately \(14\) (or in the range of \(13\) to \(15\)) score points per hour of studying.