IB Math Studies 4.2 Linear Models
Read p.147 in the textbook about “Linear models of the form 𝑓(𝑥) = 𝑚𝑥”, which is the type of model
used in conversion graphs. Below is an example of a “conversion graph” and is also problem #2 from
Exercise 4F.
Questions to think about:
-
Why are these called “conversion graphs”
What is the slope of a “conversion graph”? Why does it make sense that the y-intercept is 0?
IB Math Studies 4.2 Linear Models
Now read p.148-149 in the textbook about “linear models of the form 𝑓(𝑥) = 𝑚𝑥 + 𝑐. Below are
problems #1 and #3 from Exercise 4G, including the calculator procedures necessary for creating a
scatter plot on your GDC.
IB Math Studies 4.2 Linear Models
Whenever
you see
the
symbol, a
calculator
is
required
to
complete
the
problem
1) Enter data in your GDC by pushing the [STAT] button, selecting 1:Edit, and entering the time
data in 𝐿1 and entering the temperature data in 𝐿2 .
2) To setup the plot, push [2nd] [Y=] (STAT PLOT) and select a plot (Plot1 is fine). Then, select the
following parameters for your plot:
.
3) To graph the plot, push [ZOOM] and select 9: ZoomStat. This will automatically make the
window the right size for your data.
4) To find the linear model, push [STAT] -> CALC and select 4:LinReg(ax+b). On a TI-84, input
. On a TI-84 Plus, input as follows:
. Note: to display 𝑌1 , push [VARS]->Y-VARS and select 1:Function,
followed by 1: 𝑌1 . After this, push [ENTER] and the values for a and b will be displayed (plus r
and 𝑟 2 , but ignore these for now)
. In addtion, your GDC will store
the linear model in Y= and draw a graph of the linear model.
5) You can answer the last part of the question by plugging 85 in for x or by finding the value on
the graph – use [TRACE] or [CALC] to find this value on the graph.
IB Math Studies 4.2 Linear Models
This last problem is #1 from Exercise 4H on p.151 and is an example of linear models involving
simultaneous equations. However, the calculator procedure that the textbook shows is on a TI-Inspire.
Since we use the TI-84s, we will have to use a matrix equation to solve it. Hence, I show you the model
and the calculator procedure.
p
1) Push [2nd] [𝑥 −1 ] (MATRIX) -> EDIT and
select 1:[A]. Enter the coefficients as
follows:
[2nd] [MODE] (QUIT) when done.
2) Now, repeat this process but, instead,
select 2:[B] for matrix B
[2nd] [MODE] (QUIT) when done.
3) Finally, complete the computation:
To type in a matrix, Push [2nd] [𝑥 −1 ]
(MATRIX) -> NAMES and select the one
you want. Use the [𝑥 −1 ] key for inverse.
Now, complete the following problems as practice. You do not need to turn these in so you can
complete them in a composition notebook.
HW #4.2 p.148 Ex. 4F: 1, 3 + p.150 Ex. 4G: 2, 4 + p.152: 2-5
Your homework quiz on Thursday will still be on HW #4.1 material. We will look at quadratic models on
Thursday.