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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 :

MrRoyal

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:

[tex]y = -0.1x + 50[/tex]

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:

[tex]y = -0.1*11 + 50[/tex]

[tex]y = 49[/tex]

Hence, the number of students in year 11 is 49

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