© A Very Good Teacher 2007 Algebra 1 EOC Preparation Unit Objective 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 1, Ab1A Algebra 1 EOC Preparation Unit Objective 3:

© A Very Good Teacher 2007 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 3, Ac1A

© A Very Good Teacher 2007 Interpreting Linear Functions, cont… Example: Identify the situation that best represents the amount f(n) = n. Slope (rate of change) = Y intercept (initial value) = 3, Ac1A

© A Very Good Teacher 2007 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. 1, Ab1B

© A Very Good Teacher 2007 Functions and their equations 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. 1, Ab1B

© A Very Good Teacher 2007 Functions and their equations 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? xy , Ab1B A. y = 2x² - 4 B. y = 3x² - 4 C. y = 2x² + 4 D. y = 3x² + 4

© A Very Good Teacher 2007 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? bc , Ac1C

© A Very Good Teacher 2007 Converting Graphs to Equations Make a table of values Then, use STAT! Example: Which linear function describes the graph shown below? 3, Ac1C xy

© A Very Good Teacher 2007 Converting Equation to Graph Graph the function in y = Example: Which graph best describes the function y = -3.25x + 4? 3, Ac1C

© A Very Good Teacher 2007 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 3, Ac1C

© A Very Good Teacher 2007 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: 3, Ac2A

© A Very Good Teacher 2007 Slope and Rate of Change (m), cont… By Formula: Find two points on the graph (they won’t be given to you) 3, Ac2A

© A Very Good Teacher 2007 Slope and Rate of Change (m), cont… By Counting Find two points on the graph 3, Ac2A

© A Very Good Teacher 2007 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… 3, Ac2A Example: What is the rate of change of the function 4y = -2(x – 24)?

© A Very Good Teacher 2007 Slope and Rate of Change (m), cont… Special Cases 3, Ac2A Horizontal lines line y = 4 Have slope of zero, m = __ Have slope that is _________ Vertical lines like x = 4

© A Very Good Teacher 2007 m and b in a Linear Function Changes to m, the slope, of a line effect its steepness 3, Ac2C 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

© A Very Good Teacher 2007 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 3, Ac2C

© A Very Good Teacher 2007 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)? xy 3, Ac2D

© A Very Good Teacher 2007 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 3, Ac2E

© A Very Good Teacher 2007 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. 3, Ac2E

© A Very Good Teacher 2007 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? 3, Ac2F

© A Very Good Teacher 2007 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? 3, Ac2F