Transcript Writing a Linear Equation to Fit Data

Writing a Linear Equation to
Fit Data
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Draw a line that fits or models a set of points
Write an intercept equation that fits a set of
real-world data
A Health Connection
Part of the group will create the
graph on a Communicator® while
the other part uses their graphing
calculator.
 Both groups will set up the axes so
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saturated fat – x axis
total fat – y axis
Does the graph show a linear
pattern?
On the communicator® select the
two points (8,21) and (38,90) and
draw a line through these two
points.
Calculate the slope of this line.
Write the equation of the line in the
form y=bx. Enter this equation on
the calculator.
Adjust the y-intercept using the
intercept form for a straight line:
y=a+bx. Adjust the a value by
tenths.
 What is the real-world
meaning of the yintercept?
 What is the real world
meaning for the slope?
 Predict the total fat in
a burger with 20
grams of saturated
fat.
 Predict the saturated
fat in a burger with
50 grams of fat.
Analyzing the Exercises
 Problem 4 on page 230. Use your graphing
calculator to investigate this exercise.
 After completing the exercise discuss
 How you used the data in the problem to
determine find the value for slope (b).
 What did the value for a do to the line.
Point-Slope Form of a Linear
Equation
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Learn the point-slope form of an equation of a
line
Write equations in point-slope form that
model real-world data
 You have been writing equations of the form y
= a + bx. When you know the line’s slope and
the y-intercept you can write its equation
directly in intercept form.
 But there are times that we don’t know the yintercept.
 Some homework questions had you work
backwards from a point using the slope until
you found the y-intercept.
 We can use the slope formula to generate the
equation of a line from knowing the slope and
one point on the line.
 Since the time Beth was born, the
population of her town has increased at the
rate of approximately 850 people per year.
 On Beth’s 9th birthday the total population
was nearly 307,650. If this rate of growth
continues, what will be the population on
Beth’s 16th birthday?
 Silo and Jenny conducted an experiment in
which Jenny walked at a constant rate.
Unfortunately, Silo recorded on the data
shown in the table.
Elapse Time
(s)
Distance to the
Walker
(m)
3
4.6
6
2.8
 Silo and Jenny conducted an experiment in
which Jenny walked at a constant rate.
Unfortunately, Silo recorded only the data
shown in the table.
Elapse Time
(s)
Distance to the
Walker
(m)
3
4.6
6
2.8
 Complete steps 1-5 with your group. Be
prepared to share your thinking with the
class.
Elapse Time
(s)
Distance to the
Walker
(m)
3
4.6
6
2.8
 Consider a new set of data that describe
how the temperature of a pot of water
changed over time as it was heated.
 Some of the group should create a paper
graph while others use their graphing
calculator to create a scatter plot.
 Complete steps 6-8 with your group.
Time
(s)
24
36
49
62
76
89
Temperature
(oC)
25
30
35
40
45
50
 For step 9, compare your graph to others in
your group. Does one graph show a line
that is a better fit than others. Explain.
Time
(s)
24
36
49
62
76
89
Temperature
(oC)
25
30
35
40
45
50
 When do you use slope-intercept form and
when do you use point-slope form?
 Is there a difference between the two?
 Explain how the two forms are similar and
how they are different.
Jose’s Savings
 On Jose’s 16th birthday he collected all
the quarters in his family’s pockets and
placed them in a large jar. He decided to
continue collecting quarters on his own.
He counted the number of quarters in the
jar periodically and recorded the data in a
chart.
Jose’s Savings
 On Jose’s 16th birthday he collected all
the quarters in his family’s pockets and
placed them in a large jar. He decided to
continue collecting quarters on his own.
He counted the number of quarters in the
jar periodically and recorded the data in a
chart.
 1. Make a scatter plot of the data on your calculator.
Describe any patterns you see in the table and/or
graph.
 2. Select two points that you believe represents the
steepness of the line that would pass through the data.
(________, ________)
and
(________, ________)
 Find the slope of the line between these two points.
 Give a real world meaning to this
slope.
 Use the slope you found to write an
equation of the form y = Bx.
 Graph this equation with your
scatter plot.
 Describe how the line you graphed
is related to the scatter plot.
 What do you need to do with the
line to have the line fit the data
better?
 Run the APPS TRANFRM on your graphing
calculator. Change your equation to y=a+bx.
Press WINDOW and move up to Settings.
Change A to start at 0 and increase by steps of
10. Press GRAPH and notice that A=0 is
printed on the screen. Use the right arrow to
increase the value of A. What happens to the
graph as you increase the value of A.
 Continue to increase or decrease the value of A
until you have a line that fits the data. Write
the equation for your line.
Y = _____________________
 What is the real world meaning for the yintercept you located?
 Use your equation to predict the number of
quarters Jose will have on his 21st birthday.
Explain how you predicted the number of
quarters.
 Use your equation to predict when Jose will
have collected 1000 quarters. Explain how
you found your answer.