Let's analyze the scatter plot and approximate the equation of the line of best fit. This equation will follow the general form $y = mx + b$, where:

• $m$ is the slope of the line.
• $b$ is the y-intercept.

From the scatter plot:

1. To find $m$, select two points on the line of best fit (visually estimated).
2. Calculate the slope $m$ using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
3. Use one of the points to solve for $b$.

Next, I'll approximate the equation based on the visual appearance of the scatter plot.

Let's estimate two points from the plot:

• Point 1: $(10, 20)$
• Point 2: $(80, 90)$

Now, calculate the slope $m$: $m = \frac{90 - 20}{80 - 10} = \frac{70}{70} = 1$

Use the slope and one of the points to find $b$: $y - 20 = 1(x - 10) \Rightarrow y = 1(x - 10) + 20 \Rightarrow y = x + 10$

So, the approximate equation of the line is: $y = x + 10$

Part (b): Predicting the Quiz Score

To predict the quiz score for a student who spent 50 minutes studying: $y = 50 + 10 = 60$

Thus, the predicted quiz score is 60.

Would you like more details or explanations on any part of this? Here are some related questions that might interest you:

1. What is a line of best fit, and why is it useful?
2. How do you determine the accuracy of a line of best fit?
3. What is the correlation coefficient, and how does it relate to scatter plots?
4. How would the equation change if the points selected were different?
5. What other methods can be used to find the equation of a line of best fit?

Tip: When approximating lines of best fit, choosing points that lie directly on the visualized line can improve accuracy.