Linear Relationships Assignment Unit 3 Name:________________________ 1. For the scatter plot below, answer the following: (10 marks) 1A) Identify the dependent and independent variables. (2 marks) Dependent=__________________________ Independent = ________________________ B) Does the relationship appear to be linear or non-linear. (1 mark) Answer = ________________________ C) Draw a line of best fit. (1 mark) D) Predict what the height of a male would be for 13 years old using your line of best fit. (2 marks) Answer=__________ Interpolation or Extrapolation 1E) Predict what the height of a male would be for 21 years old using your line of best fit. (2 marks) Answer=__________ Interpolation or Extrapolation F) Will this trend continue? Explain (2 marks)
Transcript
Linear Relationships Assignment Unit 3 Name:________________________
1. For the scatter plot below, answer the following: (10 marks)
B) Does the relationship appear to be linear or non-linear. (1 mark) ________________
C) Draw a line of best fit. (1 mark)
D) Extrapolate the weight of a nine year old lobster. (1 mark) ____________
E) Interpolate the age of a 25 pound lobster. (1 mark) ____________
3. 1Identify the following patterns as linear or non-linear from the graph illustrated below. (4 marks)
1
4. For each table of values
classify the data as linear or
non-linear by finding the rate of
change. If it is linear state the
slope of the graph. (12 marks)
A)
Type: _____________
Rate of Change: ___________ Slope (if applicable): ___________
x y Differences Rate of Change
0 -70
1 -76
2 -82
3 -88
4 -94
5 -100
x y Differences Rate of Change
0 80
1 91 91-80=
2 102
3 113
4 124
5 135
B)
Type: _____________
Rate of Change: ___________ Slope (if applicable): ___________
C)
Type: _____________
Rate of Change: ___________ Slope (if applicable): ___________
x y Differences Rate of Change
0 20
1 25
2 32
3 41
4 51
5 63
5.1Identify, when graphing, whether the following data should be connected up with a
straight line (continuous) or just plotted as points (discrete). (4 marks)
RememberDiscrete data: means you can’t count fractional parts (IE people, gears on a bike,
photographs etc.)
Continuous data: means the data is connected with a straight line when graphed.
There are fractional parts to the data. (IE gas consumption in liters over 4 hours
driving).
A) The cost of each photo taken is $5 per photo __________________________
B) The cost of each student going to a movie is $8 per person_______________
C) The amount of gas consumed over driving 500 km _____________________
D) The number of songs downloaded from iTunes every hour __________________
6. 1Sketch the graphs of the following linear relations and answer the questions that follow. Be sure to fill in the table of values. (9 marks)
x y = 2x + 5 x y = -3x + 3
0 0
1 1
2 2
3 3
4 4
5 5
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
16
18
1A) For y = 2x + 5, the slope is: ______ the y-intercept = initial value is ______
B) For y = -3x +3 the slope is: ______the y -intercept= initial value is _______
C) Are these linear relations Direct or Partial?
Y = 2x + 5 is ____________________ ; while y = -3x + 3 is _____________________
7. 1Tom charges $120 to paint a room in standard duplex in Wabush or Labrador City.(9 marks)
a. Create a table of values to show how much money he would earn for the first 8 rooms.
# of Rooms Earnings
b. Is the relationship linear or nonlinear? Partial or direct?
c. Write an equation that describes the relationship between the rate of change and the amount of money he will earn.
d. 1Using your equation in C, how much money will he earn for painting 41 rooms?
8. Easy Go Cabs will charge an initial fee of $4.50 upon entering the cab. For every kilometer the cab drives thereafter, the cab will charge a rate of $1.25 per kilometer. (10 marks)
a. Create a table of values showing how much it would cost for a 10 km ride in the cab.
1
b. Is the relationship linear or non-linear? Partial or direct?
c. Write an equation that describes the relationship between the rate of change and the amount of money you will have to pay for using the cab.
Km Cost
d. Using your equation in C, how much money will you pay for a 50 km cab ride?
9. David is looking to rent a seadoo. There are two companies that rent. Company A charges $25 per hour plus a flat rate of $100 while Company B charges $75 per hour.
(11marks)
a. Write an equation for each company in the form of y = mx + b
Company A: Company B:
b. Construct a table of values for each company.
Company A Company B
x (hours) Cost y= x (hours) Cost y=0 0
1 1
2 2
3 3
4 4
c. Are the relationships linear or non-linear? Partial or Direct Variation?
Company A:
Company B:
d. 1Sketch both plans on the same x-y plane on the next page. Be sure to join the points.
10. 1A sport fishing company charges $20 plus $0.50 per word for each ad it advertises in its monthly magazine. (10 marks)
a. Write an equation to represent the cost of any ad in the form of y = mx + b.
b. Is the relationship direct or partial?
c. An add has 40 words. How much will the add cost?
d. Determine the missing values in the table below:
