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Definitions

Initial Value	The starting amount
Relation	A description of how two variables are related
Independent Variable	Values that we choose
Dependent Variable	Values that we calculate
Line of Best Fit	A line that best describes the data in a scatter plot
Variable	A symbol used to represent an unknown/unspecified value

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Need to Know

In equations:

The dependent variable (y) is represented in terms of the independent variable (x)
The rate of change (slope) is multiplied by the independent variable (x)
The initial value is a constant (plain number) that is added or subtracted

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What does that look like?

Dependent Variable Independent Variable

Initial Value Rate of Change

________ = ________ x ________ + ________

________ = ________ + ________ x ________

Fill in The Blanks

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How do we represent that?

-The independent variable goes on the x-axis

-The dependent variable goes on the y-axis

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How do we represent that?

-The vertical distance between 2 points is the rise

-The horizontal distance between 2 points is the run

-The rate of change can be found dividing the rise by the run. This is called the slope

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Intercepts

-The places where lines cross the x- and y-axis are called intercepts

- The initial value is always the y-intercept

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Tables of Values

On the Left Side

- Independent variable values

- Rise = difference between 2 values

On the Right Side

- Dependent variable values

- Run = difference between 2 values

- Initial value happens when x = 0

- The first differences are the differences between consecutive y-values

x	y
0

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TABLES OF vALUES

Run

Rise

First Differences

Initial Value

Rate of Change

Rise

Run

x	y
0

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Relationships

Ayda receives a base salary of $200 and $50 for every audio system she sells	An internet package charges a flat fee of $10 plus $0.40 per hour.
Initial Value:	Initial Value:
Rate:	Rate:
Independent Variable:	Independent Variable:
Dependent Variable	Dependent Variable

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Relationships

A Runner’s Time

Time(s)	Distance (m)
0	0
1	2
2	4
3	6
4	8

Initial Value:
Rate:
Independent Variable:
Dependent Variable

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Relationships

Cost of Renting a Bus

Initial Value:
Rate:
Independent Variable:
Dependent Variable

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Relationships

A banquet hall charges a flat rate of $300 plus $20 per person.	Lindsay earns $10 per hour.
Initial Value:	Initial Value:
Rate:	Rate:
Independent Variable:	Independent Variable:
Dependent Variable	Dependent Variable

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Relationships

Running Up The Stairs

Time(s)	Number of Stairs Climbed
0	10
1	12
2	14
3	15
4	16

Initial Value:
Rate:
Independent Variable:
Dependent Variable

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Relationships

Cost of Renting a Boat

Initial Value:
Rate:
Independent Variable:
Dependent Variable

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Get to Class!

(Absences, Final Mark)

(10, 72), (15, 65), (1, 55),

(20, 45), (3, 82), (5, 79),

(1, 92), (20, 85), (11, 60),

(7, 75), (12, 76), (2, 90),

(18, 48), (4, 88), (9, 83),

(3, 78)