Question

5. STUDENTS The table shows the number of students

at a middle school over a 10-year period.

a. Make a scatter plot of the data and draw a line of fit.

b. Write an equation of the line of fit.

c. Interpret the slope and the y-intercept of the line of fit.

d. Predict the number of students in year 11

Answer 1

The line of best fit of the student model shows the relationship between variables on a scatter plot

How to determine the equation?

The question is incomplete; So, I will make use of a dataset with the following calculation summary from a graphing calculator

• Sum of X = 112
• Sum of Y = 390.45
• Mean X = 14
• Mean Y = 48.8063
• Sum of squares (SSX) = 672
• Sum of products (SP) = -62.4
• Slope (a) = -0.1
• Y-intercept (b) = 50

So, the equation of the line of fit is:

$y = -0.1x + 50$

The slope and the y-intercept

In (a), we have:

Slope (a) = -0.1Y-intercept (b) = 50

So:

The slope means that the number of students reduces each year by a factor of 0.1, while the y-intercept means that the initial number of students is 50

The number of students in year 11

This means that x = 11.

So, we have:

$y = -0.1*11 + 50$

$y = 49$

Hence, the number of students in year 11 is 49

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