SWBAT… review the Cartesian Coordinate system & graph linear equations using a table of values Agenda 1. WU (10 min) 2. Review Cartesian Coordinate System (10 min) 3. Notes on linear equations (10 min) 4. 2 graphing examples (20 min) Warm-Up: 1. Write your HW in your planner for the week 2. Solve for y: y – 3x = Solve for y: x – 2y = 5 One Application Graphing Problem (on graph paper) Tues, 10/9

We have begun a new unit on Functions: Students will be able to: 1. Know the Cartesian Coordinate System (HW1) 2. Graph linear functions (equations) using a table of values (HW2) 3. Graph absolute value functions (HW3) 4. Graph piecewise functions (HW4) 5. Write algebraic equations given various forms of data (table, graph, words) (HW5) 6. Evaluate a function and write as an ordered pair (HW6) 7. List the domain and range of a function (HW7) 8. Determine if a relation is a function using the vertical line test or given a mapping diagram (HW8) Cell phone project after October break! Unit test after October break!

Cartesian Coordinate System Infinity HS Ms. Sophia Papaefthimiou

Objectives 1. To remember what a the Cartesian coordinate system is 2. To locate points in the coordinate system 3. To plot points in the coordinate system

The Cartesian Coordinate System The horizontal line (x-axis) is known as the ________. The vertical line (y-axis) is known as the _ _____. The point at which the axes meet or intersect is known as the _____. A coordinate system has ___ quadrants. Any point P is represented by an _ ____ _ of numbers written in the form (x, y). The __-value is always first and the __-value is always second When a point is plotted on the coordinate system, a _______ x value indicates a movement to the left. A _______ y value indicates a movement down. abscissa ordinate origin 4 ordered pair xy negative

Coordinate Plane Parts of a plane 1. x-axis 2. y-axis 3. Origin 4. Quadrants I-IV x-axis y-axis Origin ( 0, 0 ) QUAD IQUAD II QUAD IIIQUAD IV

Plotting Points 1. Remember when plotting points you always start at the origin. 2. Next you go left (if x-coordinate is negative) or right (if x-coordinate is positive. 3. Then you go up (if y-coordinate is positive) or down (if y-coordinate is negative) Plot these points: A (3, -4) B (5, 6.5) C (-4, 5) D (-7, 0) E (0, -4) F (0, -1) G (0, π) = (0, 3.14) A B C D F E G

Daniela plotted the coordinates of the 2 largest toy shops in the city. The coordinates of Shop A are (2,6). The coordinates of Shop B are in Quadrant II with the same y-coordinate as Shop A. What are the coordinates of Shop B? A. (2,0) B. (3,6) C. (4,−6) D. (-5,6) (2, 6) QUAD II

Graphing linear equations using a table of values Infinity HS Ms. Sophia Papaefthimiou

Graphing linear equations To graph a linear equation you can use: 1.) Table of values (today’s lesson) 2.) Intercepts (next unit) 3.) Slope intercept form (y = mx + b) (next unit)

What is a Linear Equation? A linear equation is an equation whose graph is a LINE. Linear Not Linear

What is a Linear Equation? A solution to the equation is any ordered pair (x, y) that makes the equation true. If we were to plot all these ordered pairs on a graph, we would be graphing a line. The equations we will be graphing have two variables, x and y. For example, The ordered pair (3, 2) is a solution since,

Ex 1: Graph y – 3x = -2 using a Table of Values x3x – 2y(x, y) Step 1: Solve for y (write y as a function of x) Step 2: Make a Table of Values

The x - values are picked by YOU! x3x – 2y(x, y) –2 –

Step 2: Make a Table of Values x3x – 2y(x, y) –23(–2) – 2-8(-2, -8) –

Step 2: Make a Table of Values x3x – 2y(x, y) –23(–2) – 2-8(-2, -8) –13(–1) – 2-5(-1, -5) 03(0) – 2-2(0, -2) 13(1) – 21(1, 1) 23(2) – 24(2, 4)

y = 3x – 2 Step 3: Plot the ordered pairs Step 4: Label the line

Ex 2: Graph x – 2y = 5 Step 1: Solve for y (write y as a function of x) x – 2y = 5 –2y = -x + 5

Step 2: Make a Table of Values xy(x, y) (-2, -3.5) -3(-1, -3) 0-2.5(0, -2.5) 1-2(1, -2) (2, -1.5) Step 3: Plot the ordered pairs Step 4: Label the line

Graphing Horizontal & Vertical Lines When you are asked to graph a line, and there is only ONE variable in the equation, the line will either be vertical or horizontal. For example, Graph x = 3 Since there are no y–values in this equation, x is always 3 and y can be any other real number. x = 3 Graph y = –2 Since there are no x–values in this equation, y is always –2 and x can be any other real number. y = –2

Application HW Problem – Do on graph paper A student makes $8 per hour at his part time job. Create a table of values and a graph to represent how much money he would earn if he worked the following hours: 15 hrs, 20 hrs, 22 hrs, 28 hrs. x (hours worked) y = 8xy (money earned) (x, y)