© A Very Good Teacher 2007 Algebra 1 EOC Preparation Unit Objective 2 Student Copy Independent and Dependent Quantities Independent and Dependent Quantities

© A Very Good Teacher 2007

Algebra 1

EOC Preparation UnitObjective 2

Student Copy

Independent and Dependent Quantities

Independent and Dependent Quantities must be variables (letters), not constants

(numbers).

Independent Quantities are often quantities that cannot be controlled

Dependent Quantities change as a result of the Independent Quantities

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Algebra 1

EOC Preparation UnitObjective 3:


Interpreting Linear Functions Functions can be represented in different ways:

y = 2x + 3 means the same thing as f(x) = 2x + 3

Linear Functions must have a ____ (rate of change) and a ________ (initial value).

In a function… the ______ is the constant (number) next to the

variable the _________ is the constant (number) by itself

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Interpreting Linear Functions, cont…

• Example: Identify the situation that best represents the amount f(n) = 425 + 50n.

Slope (rate of change) =

Y intercept (initial value) =

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Functions and their equations

• To find the equation of a function when you are given the table, use the feature of your graphing calculator.

Enter the table into the calculator using L1 for x and L2 for y.

Then return to and arrow over to CALC and choose the appropriate function type.

Press Enter to view equation.

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• How do I know what type of function to use?

• All EOC questions will either be Linear (LinReg, ax+b) or Quadratic (QuadReg)

• If you aren’t sure look at the answers and see if they are linear or quadratic.

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• Here’s one to try:The table below shows the relationship between x and y. Which function best represents the relationship between the quantities in the table?

x y

-1 -1

0 -4

1 -1

2 8

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A. y = 2x² - 4

B. y = 3x² - 4

C. y = 2x² + 4

D. y = 3x² + 4


Converting Tables to Equations• When given a table of values, USE STAT!• Example: What equation describes the relationship

between the total cost, c, and the number of books, b?

b c

10 75

15 100

20 125

25 150

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Converting Graphs to Equations• Make a table of values

• Then, use STAT!

• Example: Which linear function describes the graph shown below?

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x y


Converting Equation to Graph

• Graph the function in y =

• Example: Which graph best describes the function y = -3.25x + 4?

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Equations that are in Standard Form• Sometimes your equations won’t be in

y = mx + b form.

• They will be in standard form: __________• You must convert them to use the calculator!

Example: 3x + 2y = 12

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Slope and Rate of Change (m)• Slope and ___________ are the same thing!

• They both indicate the steepness of a line.

• Three ways to find the slope of a line:

By Formula: By Counting: By Looking:

2 1

2 1

y ym

x x

rise

mrun

y x bm

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Slope and Rate of Change (m), cont…• By Formula:

• Find two points on the graph (they won’t be given to you)

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Slope and Rate of Change (m), cont…

• By Counting

• Find two points on the graph

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Slope and Rate of Change (m), cont…• By Looking

• The equation won’t be in y = mx + b form

• You’ll have to change it• If in Standard Form use Process on Slide 7• If in some other form, you’ll have to work it out…

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Example: What is the rate of change of the function

4y = -2(x – 24)?


Slope and Rate of Change (m), cont…

• Special Cases

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• Horizontal lines line y = 4Have slope of zero, m = __

Have slope that is _________

• Vertical lines like x = 4


m and b in a Linear Function• Changes to m, the

slope, of a line effect its steepness

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• Changes to b, the y intercept, of a line effect its vertical position (up or down)

y = 1x + 0

y = 3x + 0

y = 1/3 x + 0

y = 1x + 0

y = 1x + 3

y = 1x - 4


m and b in a Linear Function, cont…

• Parallel Lines have _____ slope (m)

y = ¼ x – 3 and y = ¼ x + 6

• Perpendicular Lines have ________ _________ slope (m)

y = ¼ x – 5 and y = -4x + 15

• Lines with the same y intercept will have the same number for b

y = ¾ x – 9 and y = 5x – 9

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Linear Equations from Points• Make a table

• USE STAT

• Example: Which equation represents the line that passes through the points (3, -1) and (-3, -3)?

x y

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Intercepts of Lines• To find the

intercepts from a graph… just look!

• The x intercept is where a line crosses the x axis

• The y intercept is where a line crosses the y axis

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Intercepts of Lines, cont…• To find intercepts from equations, use your

calculator to graph them

• Example: Find the x and y intercepts of 4x – 3y = 12.

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Direct Variation• Set up a proportion!

• Make sure that similar numbers appear in the same location in the proportion

• Example: If y varies directly with x and y is 16 when x is 5 what is the value of x when y = 8?

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Direct Variation, cont…• To find the constant of variation use a

linear function (y = kx) and find the slope

• The slope, m, is the same thing as k• Example: If y varies directly with x and y = 6

when x = 2, what is the constant of variation?

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© A Very Good Teacher 2007 Algebra 1 EOC Preparation Unit Objective 2 Student Copy Independent and Dependent Quantities Independent and Dependent Quantities