Introduction to the COORDINATE PLANE

Introduction to the COORDINATE PLANE

A graph must have

- labelled x-axis

- labelled y-axis

- scale

Points on a Cartesian Plane are labelled as ordered pairs

( , )

What are the coordinates of each point?

AB

CD

Plot the following points.

E(3, 4)F(-4, -7)

G(0, 9)H(-8, 0)

I(-10, 10)O(0, 0)

When a point is on the y-axis, what does it look like?

When a point is on the x-axis, what does it look like?

Introduction to Scatter Plots and Relationships

Scatterplot

- a graph that shows the relationship between two variables

- points are not connected

Independent variable

- can be any value

Dependent variable

- changes when the independent variable changes

- depends on the independent variable

Line of Best Fit

- models the trend/pattern

- through as many points as possible

- equal points above and below the line

Outlier

- A point that does not seem to follow the trend of the data

- An unusual value

Example:

A basketball team recorded the number of points each player scored vs. the number of shots they took.

a)Identify the independent variable and the dependent variable.

b)Draw a scatter plot on graph paper and find the line of best fit.

c)Describe the correlation and the relationship between the variables.

d)If a person shot 40 times, how many points would they score? Is this interpolating or extrapolating?

e)If a person got 90 points, how many shots did they take? Is this interpolating or extrapolating?

Interpolate

Extrapolate

Which of these is the best LOBF? And what is wrong with the others?

Relationships / Correlations

- Is there a relationship between the independent and dependent variables?

- Does the value of y depend on the value of x?

Use the following words to describe correlations/relationships

- linear vs. non-linear vs. no correlation

- positive (going up) vs. negative (going down)

- weak (wide spread) vs. strong (almost straight line)

Hypothesis

- an educated guess / prediction of an expected result

- a prediction of a possible relationship

Create a hypothesis about the relationship between the amount of sunlight and plant growth.

What is the opposite of that hypothesis?

Scatterplot Worksheet

Scatterplots Day 2

State which variable is the independent and which is the dependent.

What is the relationship between the world’s population and time?

Is there a relationship between the speed of a car and the stopping distance?

Is there a relationship between the amount of alcohol consumed and response time?

Match the number with the name:

1.

2.

3.

4.

5.

6.

7.

a) Does age have a strong positive correlation with height? Explain.

b) Do you think the variables are placed appropriately on the axes?

c) Would weight vs. age show a strong positive correlation?

d) Can you think of a variable that does have a strong positive correlation with age?

e) Can you think of a variable that has a strong negative correlation with age?

Experiments

Correlation match-up sheet

Warm up

Linear and Non-Linear Relations

Step n / # of ______
1 /
2
3
4
5
10
27
100

:

Step n / # of ______
1
2 /
3
4
5
10
27
100

p. 83#1, 3, 10, 11

Challenge: #13, 14

Warm up

1) You take 2 hours to drive 550 km from London to Kingston. How fast were you driving?

2) If you are driving 90 km/h, how long will it take to drive 150 km?

Distance-Time Graphs

What is the total distance travelled in this graph?

When was the object moving the fastest? How do you know?

What is the speed for each of the intervals?

Describe what is happening in each of these distance-time graphs.

Practice: p. 91 #1 - 5, 7, 9, 11

Assignment