Math worksheet focusing on scatter plots and lines of best fit, with problems related to family income and student study time.

Problem Analysis:

The image contains a math worksheet with several tasks related to plotting data, drawing lines of best fit, and interpreting linear equations. The specific task we need to solve is Problem 4, which involves analyzing the relationship between study hours and grades.

#### Problem 4 Details:
1. Data Table:
- Study Hours: \( x \) values are \( 0, 2, 4, 6, 8, 10 \).
- Grades: \( y \) values are \( 84, 77, 92, 90, 96, 95 \).

2. Tasks:
- a) Draw a scatter plot of the data and draw the line of best fit.
- b) Write the equation for the line of best fit.
- c) Predict the grade if a student studied for 8 hours.
- d) Determine if the line of best fit can be used to predict the grade for a student who studied for 14 hours, and explain why or why not.

---

Solution:

#### Step 1: Scatter Plot and Line of Best Fit
- The scatter plot would show points corresponding to each pair \((x, y)\):
- \((0, 84)\), \((2, 77)\), \((4, 92)\), \((6, 90)\), \((8, 96)\), \((10, 95)\).
- A line of best fit is drawn through these points to represent the trend in the data. This line minimizes the distance between the points and the line.

#### Step 2: Equation of the Line of Best Fit
The equation of the line of best fit is given as:
\[
y = 0.75x + 85
\]
This equation was likely determined using statistical methods such as linear regression.

#### Step 3: Predicting the Grade for 8 Hours of Study
To predict the grade for a student who studied for 8 hours, substitute \( x = 8 \) into the equation of the line of best fit:
\[
y = 0.75(8) + 85
\]
\[
y = 6 + 85
\]
\[
y = 91
\]
So, the predicted grade for 8 hours of study is 91.

#### Step 4: Predicting the Grade for 14 Hours of Study
To determine if the line of best fit can be used to predict the grade for a student who studied for 14 hours, substitute \( x = 14 \) into the equation:
\[
y = 0.75(14) + 85
\]
\[
y = 10.5 + 85
\]
\[
y = 95.5
\]
However, this prediction may not be reliable because:
- The data provided only includes study hours up to 10 hours.
- Extrapolating beyond the range of the data (i.e., using the line of best fit for values outside the observed range) can lead to inaccurate predictions.
- There may be other factors affecting grades that are not captured by the linear relationship within the observed range.

Thus, while the mathematical calculation gives \( y = 95.5 \), it is generally not advisable to use the line of best fit for extrapolation beyond the observed data range.

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Final Answers:

1. Equation of the line of best fit: \( y = 0.75x + 85 \)
2. Predicted grade for 8 hours of study: \( 91 \)
3. Predicted grade for 14 hours of study: \( 95.5 \) (but not reliable due to extrapolation)

\[
\boxed{91}
\]