## Graphing Vocabulary

Match the words in the following word list to each of the seven definitions given below.

Dependent Variable

Extrapolation

Independent Variable

Interpolation

Line of Best Fit

Linear

Non-Linear

**Definition **

When the points on a scatter plot appear to follow a straight line.

**Notable Notes **

The points do not need to form a perfectly straight line.

**Non Examples **
**Examples **

**Definition **

The variable in an experiment that is controlled.

**Notable Notes **

Graphed on the x-axis.

**Examples **

Time

**Non Examples **

Depth of Water

**Definition **

The variable in an experiment that is measured or observed.

**Notable Notes **
This is what you are most interested in

measuring in an experiment.

Graphed on the y-axis.

**Non Examples **

Time
**Examples **

**Definition **

Predicting a value outside of your data set.

**Notes **

**Non Examples **

How many visitors were there
when it was 83o_{? }

**Examples **

How many visitors were there

when it was 80o_{? }
**Definition **

When the points on a scatter plot appear to follow a curve or have no pattern at all.

**Notes **

**Non Examples **
**Examples **

**Definition **

A straight line that models the trend shown by your data.

**Notes **

This can be used to make predictions based on your data.

**Non Examples **
**Examples **

**Definition **

Predicting a value inside of your data set.

**Notes **

**Non Examples **

How many visitors were there
when it was 104o_{? }
**Examples **

How many visitors were there

**0**
**2**
**4**
**6**
**8**
**10**
**12**
**14**
**16**
**18**
**20**

**0** **20** **40** **60** **80 100 120 140**

**Speed (km /h)**

**F**
**u**
**e**
**l **
**C**
**o**
**n**
**s**
**u**
**m**
**p**
**ti**
**o**
**n**
** (**
**L**
** p**
**e**
**r **
**1**
**0**
**0**
**k**
**m**
**)**

### Scatter Plots & Trends

For each of the following graphs, circle any outliers, identify the independent and dependent variables, identify whether it is a linear or non-linear relationship, and state the trend.

a)

Independent Variable: ______________________________

Dependent Variable: ______________________________

Linear / Non-Linear

Trend:

b)

Independent Variable: ______________________________

Dependent Variable: ______________________________

Linear / Non-Linear

Trend:

c)

Independent Variable: ______________________________

Dependent Variable: ______________________________

Linear / Non-Linear

Trend:
**0**
**20**
**40**
**60**
**80**
**100**

**0** **5** **10**

**Number of Cars Washed**

**M**
**o**
**n**
**e**
**y**
** Ea**
**rn**
**e**
**d**
**0**
**4**
**8**

**0** **1** **2** **3** **4** **5** **6**

**Height of Skateboard Ramp**

**0**
**5**
**10**
**15**
**20**
**25**
**30**

**0** **2** **4** **6** **8** **10** **12**

**0**
**5**
**10**
**15**
**20**
**25**
**30**
**35**
**40**

**0** **2** **4** **6** **8** **10** **12**

**0**
**10**
**20**
**30**
**40**
**50**
**60**
**70**
**80**

**0** **2** **4** **6** **8** **10** **12**

**0**
**20**
**40**
**60**
**80**
**100**
**120**

**0** **2** **4** **6** **8** **10** **12**

**0**
**10**
**20**
**30**
**40**
**50**
**60**
**70**
**80**
**90**
**100**

**0** **2** **4** **6** **8** **10** **12**

### Line of Best Fit

1. For each of the following graphs, determine if the graph is linear or non-linear. If it is linear, draw a line of best fit.

a)

Linear / Non-Linear

b) c)

Linear / Non-Linear Linear / Non-Linear

d) e)

Linear / Non-Linear Linear / Non-Linear

**A good line of best fit… **

Follows the trend

Is in the middle of the data (same # of points above and below)

Extends from one end of the grid to the other

2. The following table shows the number of students that have applied to Ontario Universities each year since 2004.

**Year ** **# of Students Applying **

2004 71771

2005 73956

2006 76300

2007 80362

2008 83813

2009 84691

2011 89181

2012 90889

a) Identify the independent variable.

b) Identify the dependent variable.

c) What does the zig-zag on the x-axis mean?

d) What is one square worth on the x-axis?

e) What is one square worth on the y-axis?

f) How did the person making the graph decide where to put the point for 2011?

g) One of the points is plotted incorrectly. Which one is it? Correctly plot the point.

h) Draw in a line of best fit.

i) Using your line of best fit, predict the number of students that applied in 2016. Is this an example of interpolation or extrapolation?

j) Using your line of best fit, predict the number of students that applied in 2010. Is this an example of interpolation or extrapolation?

**40000**
**50000**
**60000**
**70000**
**80000**
**90000**
**100000**
**110000**
**120000**
**130000**

**2002** **2004** **2006** **2008** **2010** **2012** **2014** **2016** **2018** **2020** **2022**

**Year**

**# **

**of**

** S**

**tud**

**ent**

**s **

**App**

**ly**

**ing t**

**o O**

**nt**

**ar**

**io Univ**

**er**

**si**

**tie**

### Scatter Plots, Trends, & Line of Best Fit Homework

1. The following scatter plot shows the average temperature of the ocean as a function of the latitude, in the southern hemisphere.

a) State the independent and dependent variables.

*Independent: *

*Dependent: *

b) State the trend shown by this graph.

c) Draw a line of best fit.

d) Predict the average temperature of the ocean
at a latitude of 35o_{S. Is this an example of }
interpolation or extrapolation?

e) Predict the average temperature of the ocean
at a latitude of 55o_{S. Is this an example of }
interpolation or extrapolation?

f) At what latitude would you expect the average
temperature to be 2 o_{C? Is this an example of }
interpolation or extrapolation?

g) At what latitude would you expect the temperature to be 17 o_{C? Is this an example of interpolation or }
extrapolation?

**Ocean Temperature **
**(Southern Hemisphere)**

**0**
**2**
**4**
**6**
**8**
**10**
**12**
**14**
**16**
**18**
**20**
**22**
**24**
**26**
**28**

**0** **10** **20** **30** **40** **50** **60** **70** **80** **90**

**Latitude (S)**

**Te**

**mp **

2. The following graph represents the relationship between the **final exam mark (%) and the number **
**of hours of sleep that a student got before their exam. **

a) Identify the independent variable. Justify your choice.

b) Identify the dependent variable. Justify your choice.

c) Label the x and y axes appropriately based on your answers from a) and b).

d) What does each square represent on the x-axis?

e) What does each square represent on the y-axis?

f) Fill in the following table of values using the graph:

g) State the trend shown by the graph. h) Draw a line of best fit and predict what

mark you think someone who got 4 hours of sleep should get. Is this an example of interpolation or extrapolation?

**Number of **
**Hours of Sleep **

**Final Exam **
**Mark (%) **

0 10 20 30 40 50 60 70 80 90 100

3. The following table of values shows the height of a balloon versus time.

**Time (s) ** **Height (m) **

2 5

4 7

6 10

8 13

10 18

12 21

14 24

16 25

18 27

20 30

a) Create a scatter plot.

b) State the trend shown by the graph.

c) Draw a line of best fit.

d) Predict the height of the balloon after 9 seconds.

e) Is your answer to d) an example of interpolation or extrapolation?

f) Predict how long it would take for the balloon to reach a height of 40 m.

g) Is your answer to f) an example of interpolation or extrapolation?

h) How high above the ground was the

balloon when it was released?

**0**
**2**
**4**
**6**
**8**
**10**
**12**
**14**
**16**
**18**
**20**
**22**
**24**
**26**
**28**
**30**
**32**
**34**
**36**
**38**
**40**
**42**
**44**
**46**
**48**
**50**

**0** **2** **4** **6** **8** **10 12 14** **16 18 20 22 24 26 28 30**

**Time (s)**

**H**

**e**

**ig**

**h**

**t **

**(m**

0 5 10 15 20

0 5 10 15 20

4. The following table shows the number of chin-ups that a student can do, compared to their age.

a) Determine the independent and dependent variables. Label them on the appropriate axes on the graph.

*Independent: *

*Dependent: *

b) Create a scatter plot of the data in the table.

c) State the trend shown by the graph.

d) Stacey can do 18 chin-ups. How old do you think she is?

e) Is your answer from d) an example of interpolation or extrapolation?

f) Tahir is 6 years old. How many chin-ups would you expect him to be able to do?

g) Is your answer from f) an example of interpolation or extrapolation?

ANSWERS:

**1a]** *Independent*: Latitude, *Dependent*: Temperature **1b]** As the latitude increases, the temperature of the water decreases **1d]** *(Answers Will Vary)* 12.5 o_{C }

**1e ]*** (Answers Will Vary) *5.3 oC **1f]** *(Answers Will Vary)* 64 oS **1g]** *(Answers Will Vary)* 23 oS **2a]** Hours of Sleep – this is the variable that you would
have some control over **2b]** Final Exam Mark – this is what we are more interested in measuring **2c]** *X-Axis*: Hours of Sleep, *Y-Axis*: Final Exam Mark

**2d]** 1 hour of sleep **2e]** 5% on the exam **2f]** (0, 30), (1, 92), (2, 40), (2.4, 45), (3, 55), (5, 55), (5, 65), (6, 70), (8, 84), (9, 25), (10, 95), (11, 90) **2g]** As the
hours of sleep increases, the final exam mark increases **2h]** *(Answers Will Vary)* 56%, Interpolation **3b]** As time increases, the height of the balloon
increases **3d]** *(Answers Will Vary)* 15.2 m **3e]** Interpolation **3f]** *(Answers Will Vary)* 26 sec **3g]** Extrapolation **3h]** *(Answers Will Vary)* 2 m

**4a]** *Independent*: Age, *Dependent*: Number of Chin-Ups **4c]** As age increases, the number of chin-ups that a student can do increases **4d]** *(Answers Will *
*Vary) *19.5 years old **4e]** Extrapolation **4f]** *(Answers Will Vary)* 1 chin-up **4g]** Extrapolation

**Age ** **Number of **

**Chin-Ups **

10 8

11 8

12 8

13 11

15 13

14 11

13 9

17 14

13 10

14 12

16 14

17 16

10 7

16 15

10 7