Section 3.1: Introduction to Linear Equations in 2 Variables Section 3.2: Graphing by Plotting Points and Finding Intercepts

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1 Remember to read the tetbook before attempting to do our homework. Section 3.1: Introduction to Linear Equations in 2 Variables Section 3.2: Graphing b Plotting Points and Finding Intercepts Rectangular Coordinate Sstem aka Cartesian coordinate sstem, aka -plane The -ais (horizontal ais) and -ais (vertical ais) divide the plane into four quadrants (regions): Quadrant 2 (, + ) Quadrant 1 ( +, + ) The graph of an ordered pair, (, ), is a point where the 1 st number is called the -coordinate, the 2 nd number is called the -coordinate. Things to note: The origin is the point where the -and -ais meet. The coordinates of the origin are given b (0, 0). The points on the -ais or -ais do not belong to an quadrant. Origin Quadrant 3 (, ) The order of the numbers is ver important, e.g. (2, 5) is not the same as (5, 2) (0, 0) Quadrant 4 ( +, ) Eample 1: a. Is (3, 5) a solution of 2 3 = 9? b. Is (5, 3) a solution of 2 3 = 9? Eample 2: Graph the following set of ordered pairs and label the coordinates of the points: {(0, 0), ( 1, 3), (0, 5), (5, 0), (3.5, 4), ( 3, 4)} Friendl Reminder: Ordered pairs are written in the form (, ). To graph an ordered pair, first start from the origin, and then See how man units ou should move to the left or right (this is determined b the -coordinate) 2. See how man units ou should move up or down (this is determined b the -coordinate) Math 60 Beginning Algebra Cerritos College Pg 1 Chapter 3 Lecture Notes b Maria Torres

2 Standard Form A linear equation in 2 variables written in the form A + B = C, is said to be in standard form, where A, B, and C are real numbers (A and B not both 0). In English: Fi the equation so ou have the -term + -term = constant term. Also, please make sure that ou have integer coefficients. Question: I know that the graph of an ordered pair is a point, but what does the graph of a linear equation look like? Answer: A straight line. Question: How do ou graph of a line? Answer: Oh that s eas! Just find 2 ordered pair solutions of the equation, graph them, and then connect the points. Question: Is there an eas wa to find ordered pair solutions? Answer: Of course there is! Just Solve the equation for, then 2. Create an -table, and then 3. Pick a value for and find the corresponding value for. E 3: Graph b plotting at least 3 points for each graph. You ma not use a calculator to answer. a = 4 b. 4 = 3 9 Math 60 Beginning Algebra Cerritos College Pg 2 Chapter 3 Lecture Notes b Maria Torres

3 Question: Is there a different wa to obtain the graph of a line? Answer: Yes, there is! We can also graph a line b using the -intercept and the -intercept. Intercepts of a Line -intercept: The point where the line intercepts the -ais. To find the -intercept: Let = 0, and then Solve for. Note: The -intercept is of the form (1, 0) -intercept: The point where the line intercepts the -ais. To find the -intercept: Let = 0, and then Solve for. Note: The -intercept is of the form (0, 1) Since the graph intercepts the -ais at 1, then -int = (1, 0) Since the graph intercepts the -ais at 2, then -int = (0, 2) Eample 4: What is the -intercept? What is the -intercept? Use the -intercept and -intercept to graph the line. Label the coordinates of the intercepts. a = 20 b = 7 Bored or just looking for more fun? Then work on the attached Xtra Practice Sheet (intercepts) Math 60 Beginning Algebra Cerritos College Pg 3 Chapter 3 Lecture Notes b Maria Torres

4 Xtra Practice: Using intercepts to graph linear equations Sample: Use the intercepts to graph 2 3 = 6. On our graph, please label the coordinates of the intercepts. Solution: Goal #1: Find the -intercept Goal #2: Find the -intercept Goal #3: Use the intercepts to graph the line. To find the -intercept: Let = 0, then solve for. 2 3 = 6 2 3(0) = 6 2 = 6 = 3 To find the -intercept: Let = 0, then solve for. 2 3 = 6 2(0) 3 = 6 3 = 6 = 2 ( 3, 0) (0, 2) P.S. -intercept: ( 3, 0) -intercept: (0, 2) Don t forget to label the intercepts Directions: What is the -intercept? What is the -intercept? Use the -intercept and -intercept to graph the line. Label the coordinates of the intercepts a. 5 6 = 30 b. 8 4 = 32 Math 60 Beginning Algebra Cerritos College Pg 4 Chapter 3 Lecture Notes b Maria Torres

5 c. 4 = 4 + d. 5 = 35 7 e. 18 = 2 f. = (Solutions will be posted on the Math 60 page) Math 60 Beginning Algebra Cerritos College Pg 5 Chapter 3 Lecture Notes b Maria Torres

6 Vertical and Horizontal Lines The graph of an equation of the form The graph of an equation of the form = 1 is a vertical line that intercepts the -ais at 1. = 1 is a horizontal line that intercepts the -ais at 1. Moral of the stor: If an equation does not contain BOTH and variables, then the graph of the equation will be either a vertical line or a horizontal line. Eample 5: Graph = 2 Psst psst... The graph of = 2 is a vertical line that intercepts the -ais at positive 2. Eample 6: Graph = 3 Psst psst... the graph of = 3 is a horizontal line that intercepts the -ais at negative 3. Eample 7: Graph the lines. a. + 3 = 0 b. 8 = 0 c = 2 d = 2 (end of Section 3.1/3.2 combo) Math 60 Beginning Algebra Cerritos College Pg 6 Chapter 3 Lecture Notes b Maria Torres