Modelling with Linear Functions

  1. For each of the following tables of \((x,y)\)-pairs plot a scatter plot for the table in Desmos. Press the l’il magnifying glass icon near the table to automatically fit the viewport to the scatter plot. Then press the l’il “regression” icon to determine the line the best fits the points in the table. Compare this line to the one you estimated a week-or-so ago when you first plotted scatter plots for these tables of \((x,y)\)-pairs. Also take note of the \(R^2\) value Desmos reports; the closer \(R^2\) is to \(1,\) the better the line fits the scatter plot.

    \(x\) \(y\)
    0 3
    1 5
    2 7
    \(x\) \(y\)
    1 -1
    2 0
    3 2
    \(x\) \(y\)
    -1 0
    2 -3
    5 3
    \(x\) \(y\)
    9 -10
    1 4
    -6 12
    \(x\) \(y\)
    9 45
    23 0
    67 23
    \(x\) \(y\)
    2 21
    5 33
    9 49
    \(x\) \(y\)
    1 -6
    17 1
    24 5
    \(x\) 1 2 3 4 5 6
    \(y\) 0 2 1 3 7 6
    \(x\) 0 10 20 30 40 50 60 70 80
    \(y\) -15 6 21 41 58 69 88 105 121

  2. Interpolate – This table lists the high temperatures recorded each day during the first week of March 2021, but the value of March 5 is missing. Using the linear model that best fits the available data, what was likely the high temperature on March 5, 2021?

    Day of March 1 2 3 4 5 6 7
    Temperature (°F) 47 54 62 54 64 67

  3. Extrapolate – Today I started a road trip. This table lists the odometer reading in my truck each hour since I started. Using the linear model that best fits the available data, and assuming I continue my road trip at approximately the same average speed, what can be predict the odometer will read at the 8-hour mark?

    Hours Elapsed 0 1 2 3 4 … 8
    Odometer Reading (miles) 0 75 144 213 288 …