Linear Relationships and Models
Objectives:
To be able to determine if data represents a linear relationship
To review the equation of a line: y=mx+b (slope intercept form)
PART A
Scenario: Carlo had $12 saved in pocket money. He spends $2 each day at the canteen. How much money does he have
left after any given day?
Which is the independent variable? ____________________________________
Which is the dependent variable? _____________________________________
Construct a table of values which connects the diagram number x, to your measurable quantity, y.
X
0
1
2
3
4
5
6
7
Y
Write an equation that shows how to predict y, given that we know x. ___________________________________
Explain in words what this equation means.
12 y
Graph the table-of-values on the graph, clearly labeling the
axes.
10
8
Also plot the points on the GDC by going to
6
STAT – EDIT and enter the x data as L1 and
4
the y data as L2
2
x
Can x be a negative number in the scenario? Explain your
answer.
Can y be a negative number? Explain your answer.
–2
2
–2
4
6
8
What sort of shape does your graph resemble? Explain how you can tell from the table-of values.
Can you predict what y would be in the 10th diagram? Show how you could make this prediction.
Use your GDC to justify your prediction above. How could I do this?
PART B
Which of these tables-of-values represent Linear Relationships? Use your answers from above to explain?
1
2
x 0 1 2 3 4 5
y 0 2 4 6 8 10
3
x 0 1 2 3 4 5
y -8 -5 -2 1 4 7
4
x 0 1 2 3 4 5
y 9 7 5 3 1 -1
5
x 0 1 2 3 4 5
y -5 -3 -1 1 3 5
6
x 0 1 2 3 4 5
y 1 4 6 7 8 10
x 0 1 2
y 9 8 7
Justify your answers as you work through these questions by using your GDC.
3 4 5
6 5 4
Which linear relationship is steeper between tables 1 and 2? How can you tell from the data?
What are the similarities / differences between the linear data in tables 1 and 3?
What are the similarities /differences between the linear data in table 1 and 4?
What are the similarity /difference between the linear data in table 3 and 6?
Can you find an equation to model these linear relationships? What are the similarity/differences with the
equations?
Write the equations next to the table.
NOTES: The equation of a line may be represented by the equation;
PART C – Modeling Exploration
Property Investment
Verbal Description:
Ms. M has a summer cottage for which she paid $120,000. Each
year, the value of the house increases by $8,000.
Data Table:
x
y
Graph:
Equation:
Slope:
Meaning of Slope:
Y-intercept:
Meaning of y-intercept :
Questions:
(a) When will my cottage be worth $200,000?
(b) What will be the value of my cottage in 4 years time?
(c) When will the value of my cottage be double its original value?
(d) At what rate is the value of the house changing from year to year?
(e) What is the x-intercept and what does it mean?
Income & earnings
Verbal Description:
John works at a clothing store and his weekly salary is $300
and he earns 5% commission on his weekly sales.
Data Table:
sales
0
1000
2000
3000
4000
5000
earnings
Graph:
Equation:
Slope:
Meaning of Slope:
Y-intercept:
Meaning of y-intercept :
Questions:
(a) When will John’s earnings be $700?
(b) What will be John’s earnings if he sells $6,525 worth of clothing?
(c) John gets a raise in pay and now earns a base salary of $500, but his commission remains at 5% of total sales. Write
a new equation and graph it on the grid. What is similar about the 2 graphs? What is different about the 2 graphs.
(d) John now gets a raise in pay. He stills earns a base salary of $300, but his commission is now 10% Write a new
equation and graph it on the grid. What is similar about the 2 graphs? What is different about the 2 graphs.
(e) John now gets promoted to Store Manager and earns a weekly salary of $1100. and graph it on the grid. What does
this graph look like?
PART D
With a partner, you will work on one question below. Together you will work through that question and present the solution
suitably on a poster. Be prepared to explain your scenario to another group or to the class! Write the scenario in words before
working through the questions.
3.
4.