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Vocabulary
Linear Functions
Independent & Dependent
What is it?
Is it a Function?
100
What is the definition of domain?
A set of input values (all values of x).
100

Rate of change of y = -2x+3

-2

100

You and a friend are studying for a quiz. You want to get a higher score than your friend, so you decide to spend exactly 20 more minutes studying than your friend does. The relationship between these two variables can be expressed by the equation y=x+20, where x is the number of minutes your friend spends studying, and y is the number of minutes you spend studying. Identify the independent (x) and dependent (y) variables.

Independent (x) Variable: The number of minutes your friend spends studying. Dependent (y) Variable: The number of minutes you spend studying.

100
Linear or Nonlinear
xy
3
5
7		7
9
11

Linear

100
Is it a function? Justify your answer. {(2, 3), (4, 5), ( -2, 6)}
Yes, each input has exactly one output.
200
What is the definition of range?
The set of output values (all values of y).
200

Find the slope.

(-1,3) (3, 4)

1/4

200

Identify the independent (x) variable: The relationship between the number of hours worked and the amount of money earned.

The number of hours worked.

200

State Linear or nonlinear 

Nonlinear

200
Using the vertical line test, does the graph of the points (1,3) and (1,5) represent a function?
No, the points fail the Vertical Line Test.
300
What is the definition of a function?
A relationship between input and output values. Each input has exactly one output value.
300

Find slope.

(-3, 5) (6, 5)

0

300

Identify the dependent (y) variable: The relationship between your allowance and the number of chores you do.

Your allowance.

300

State linear or nonlinear 

Nonlinear

300
Is it a function? Justify your answer.
x y
2 4
1 5
2 6
No, the input of 2 has two different outputs.
400

Which variable is the input, and which one is the output? 

(Which one is the x-variable, which one is the y-variable?)

x-variable is the input, y-variable is the output

(x - independent, y - dependent)

400

Write a linear equation in slope intercept form:

slope = -4 

containing the point (0, 5)

y = -4x + 5

400

Identify the independent (x) and dependent variables (y): You are buying boxes of cookies at a bakery. Each box of cookies costs $4.

Independent Variable: The number boxes of cookies purchased. Dependent Variable: How much you spend at the bakery.

400

State if from x = -1 to x = 1 is increasing or decreasing. 

Increasing

400
Is it a function? Justify your answer.
Yes, it passes the Vertical Line Test.
500
What is the test to tell if a graph is a function?
Vertical Line Test
500

Write a linear equation in slope intercept form given two points.

(2, 5) (3, 7)

y = 2x + 1

500

Identify the independent (x) and dependent (y) variables: On your math quiz, you earn 5 points for each question that you answer correctly.

Independent Variable: Number of questions answered correctly. Dependent Variable: Score on the quiz.

500

State whether the function increasing or decreasing and linear or nonlinear between x = -4 to x = -1.

Decreasing Nonlinear

500
Is it a function? Justify your answer.
Yes, each input has exactly one output.