Algebra Ii/Trig Dickinson-Ross

Algebra Ii/Trig Dickinson-Ross

ALGEBRA II/TRIG

LINE OF BEST FIT ACTIVITY

  1. Using the data in the table below plot all ordered pairs on the graph paper supplied. Choose appropriate scales on your x- and y-axes to accommodate the data. Make sure the units are proportional.

x = time in seconds / 10 / 15 / 20 / 25 / 30 / 35 / 40
y = temperature in Celsius / -3 / 5 / 6 / 11 / 14 / 18 / 24
  1. Pick two points from your scatterplot to draw a line that you feel best fits the data points you have graphed. Circle the 2 points and draw a linethrough those two points.
  1. Use the point-slope formula to determine the equation of this line. Give the final answer in slope-intercept form. Show work.
  1. Fill in the table below with the appropriate data. You can use your calculator to help.

First, to clear all lists in your calculator, hit 2nd “+” for Memory menu, then 4: ClrAllLists ENTER. Then, to enter the data:

  1. STAT, EDIT, put x values in L1 and y values in L2
  2. Put cursor directly on L3(arrow to top of column) and type L12, ENTER
  3. Put cursor directly on L4 and type L1*L2
  4. To find averages: 2nd, LIST, MATH, 3:MEAN, then type L1 to find the average of x. Do the same for the other lists.

Average(to the nearest tenth)

x / 10 / 15 / 20 / 25 / 30 / 35 / 40
y / -3 / 5 / 6 / 11 / 14 / 18 / 24
x2
xy

5. Using the system of equations:y = mx + b ______

xy = mx2 + bx ______

Replace y in the top equation with the average of the y’s

Replace x in the top equation with the average of the x’s

Replace xy in the bottom equation with the average of the xy’s

Replace x2 in the bottom equation with the average of the x2’s

Replace the x in the bx term in the bottom equation with the average of the x’s

  1. Solve the resulting two equations for m and b using any method, and substitute these into

the equation:

y = mx + b ______

You have just computed the line of best fit for the given data.

  1. A third way to do this is to use the calculator again.
  1. Make sure your original data is still in L1 and L2.
  2. STAT, CALC, 4:LinReg L1,L2
  3. State the equation that appears.

______Use the numbers with allthe decimal places. This is the line of best fit.

  1. Predict the temperature at 17 seconds, using each of the three lines.

From #3 ______

From #6 ______

From #7 ______

Which answer do you think is the best? ______

  1. When do you think the temperature will be at 35oC? Use equation from #6. Show work and give your answer to the nearest tenth.

______

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