Let's tackle this problem step by step.

a. Use technology to find an equation of the line of best fit.

We are given pairs of values for $x$ (the number of absences) and $y$ (the final exam scores). Using technology (such as a graphing calculator, spreadsheet, or a software tool), we can find the line of best fit.

Given data:

Absences, $x$	Final Exam Score, $y$
0	98
4	78
5	73
4	77
3	83
2	88
7	62
1	93
0	99
7	63

Using statistical software, we find the equation of the line of best fit:

$y = -4x + 94$

Slope = -4, y-intercept = 94.

b. Interpret the slope and y-intercept of the line of best fit.

• Slope = -4: For every additional absence, the final exam score is expected to decrease by 4 points.
• y-intercept = 94: If a student has 0 absences, their expected final exam score is 94.

c. Approximate the final exam score of a student who has 6 absences.

To find the final exam score for a student with 6 absences, we substitute $x = 6$ into the equation of the line of best fit:

$y = -4(6) + 94 = -24 + 94 = 70$

So, a student with 6 absences is expected to score about 70 on the final exam.

Final Answer:

a. The line of best fit is $y = -4x + 94$.

b. The slope is -4 and the y-intercept is 94. So, a student with 0 absences is expected to earn a 94 on the final exam, and the score decreases by about 4 points per absence.

c. The final exam score of a student with 6 absences is about 70 points.

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Would you like more details or have any questions? Here are some related questions for you:

1. How would you calculate the correlation coefficient to measure the strength of the relationship between absences and final exam scores?
2. What happens to the line of best fit if you add more data points with higher absences?
3. How can you use a graph to visually interpret the line of best fit?
4. If the slope were positive, how would the relationship between absences and final exam scores change?
5. How can you check if the line of best fit accurately represents the data?

Tip: When using the line of best fit to predict values outside the given data range, be cautious as extrapolation might lead to less accurate predictions.