Unit D: Graphing

The line of best fit is extremely useful to estimate values on a scatterplot. Interpolation is one way to estimate values based on the line of best fit.

Use the line of best fit to estimate the y-value when x = 8.







The y-value is approximately 16.5 when x = 8 using the method of interpolation.
Extrapolation is another way to estimate values based on the line of best fit.

Use the line of best fit to estimate the x-value when y = 2.




The first step is to extend the line of best fit.




Now use extrapolation to find the x-value when y = 2.




The x-value is approximately 1 when y = 2.
The amount of time math students spend on homework is compared to the students' test marks. The data is recorded on the graph below.




  1. Does the scatterplot show positive correlation, negative correlation or no correlation?

  2. Draw the line of best fit.

  3. What trend is displayed on the scatterplot?

  4. Estimate the time spent on homework if a student received a test mark of 85%.

  5. Estimate the test mark if a student spent 0 hours completing homework.

  1. The graph shows positive correlation since the points form the shape of a line that rises from left to right.

  2. There is some flexibility when drawing the line of best fit. The stronger the correlation, the easier it is to draw an accurate line of best fit. Make sure that the line of best fit is in the middle of the points and that there are approximately the same number of points above the line as below the line.




  3. As the time spent on homework increases, the test mark increases.




  4. If a student received a test mark of 85%, using interpolation, the student spent approximately 7 hours completing homework.




  5. If a student spent 0 hours completing homework, the student would receive a test mark of approximately 46%. This mark is determined by extending the line and using extrapolation.
A farmer sells his apples daily at a farmer's market. The graph shows the pounds of apples sold compared to the price the consumers pay for the apples.




  1. State if the scatterplot shows positive correlation, negative correlation or no correlation.

  2. Draw the line of best fit.

  3. What trend is displayed on the scatterplot?

  4. Estimate the pounds of apples sold if the price of apples is $1.20/lb.

  5. What would the price of the apples be if the farmer sells 20 pounds?

  1. The graph shows negative correlation since the points form the shape of a line that falls from left to right.

  2. There is some flexibility when drawing the line of best fit. The stronger the correlation, the easier it is to draw an accurate line of best fit. Make sure that the line of best fit is in the middle of the points and that there are approximately the same number of points above the line as below the line. The outlier is not considered when drawing the line.




  3. As the price of apples increases, the pounds of apples sold decreases.




  4. If the price is $1.20/lb, approximately 11 pounds of apples will be sold. This is determined by using interpolation.




  5. If 20 pounds of apples are sold, the cost of the apples would be approximately $0.30/lb. This is determined using extrapolation.
A convenience store sells daily newspapers. The manager would like to determine if the outside temperature affects newspaper sales.




  1. Does the scatterplot show positive correlation, negative correlation, or no correlation?

  2. Draw the line of best fit.

  3. What trend is displayed on the scatterplot?

  1. The graph shows no correlation between the outside temperature and the number of newspapers sold since the shape of a line cannot be seen in the graph.

  2. No relationship exists between the two variables. The line of best fit cannot be drawn for a scatterplot with no correlation.

  3. There is no trend in the data as the points are scattered throughout the graph.