1. Place your test corrections in the blue folder Thurs, 9/15 SWBAT… review the Cartesian Coordinate system & graph linear equations using a table of values Agenda WU (10 min) Brain Pop video – Cartesian Coordinate System (10 min) Notes on linear equations w/ practice problems (25 min) Warm-Up: 1. Place your test corrections in the blue folder 2. Solve for y: x – 2y = 5 HW#1: Cartesian Coordinate System and HW#2: Graphing Linear equations

Cartesian Coordinate System Infinity HS Ms. Sophia Papaefthimiou

Objectives To remember what a the Cartesian coordinate system is To locate points in the coordinate system To plot points in the coordinate system

Brain Pop Video

A Coordinate System The horizontal line is known as the _____. The vertical line is known as the ______. The point at which the axes meet or intersect is known as the _____. A coordinate system has ___ quadrants. Abscissa Ordinate Origin 4

Coordinate Plane QUAD II QUAD I QUAD III QUAD IV y-axis Parts of a plane x-axis y-axis Origin Quadrants I-IV QUAD II QUAD I Origin ( 0 , 0 ) x-axis QUAD III QUAD IV

Plotting Points Plot these 4 points: A (3, -4) B (5, 6.5) C (-4, 5) 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) B C D A Plot these 4 points: A (3, -4) B (5, 6.5) C (-4, 5) D (-7, 0)

Locating Points RULE: Any point P is represented by an ordered pair of numbers written in the form (x, y) The x-value is always first and the y-value is always second

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 project) 3.) Slope intercept form (y = mx + b) (next project)

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

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

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

The x - values are picked by YOU! Table of Values x 3x – 2 y (x, y) –2 –1 1 2 The x - values are picked by YOU!

Table of Values x 3x – 2 y (x, y) –2 3(–2) – 2 -8 (-2, -8) –1 1 2

Table of Values x 3x – 2 y (x, y) –2 3(–2) – 2 -8 (-2, -8) –1 3(–1) – 2 -5 (-1, -5) 3(0) – 2 -2 (0, -2) 1 3(1) – 2 (1, 1) 2 3(2) – 2 4 (2, 4)

y = 3x – 2 y x

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

Second Step: Make a Table of Values y x x y (x, y) -2 -3.5 (-2, -3.5) -1 -3 (-1, -3) -2.5 (0, -2.5) 1 (1, -2) 2 -1.5 (2, -1.5)

Graphing Horizontal & Vertical Lines y x 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 y = –2 Since there are no y–values in this equation, x is always 3 and y can be any other real number. Graph y = –2 Since there are no x–values in this equation, y is always –2 and x can be any other real number. x = 3