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MATH 0960 7.1 Notes CHAPTER 7: Graphing Linear Equations Section 7.1: The Cartesian Coordinate System and Linear Equations in Two Variables Topics: A. Plot points in the Cartesian coordinate system. B. Determine whether an ordered pair is a solution to a linear equation. C. Solve applications. A. Plot points in the Cartesian coordinate system. What does a problem look like? Example: Plot the following points on the same axes. Make sure you label your axes and points. 1. ( ) 2. ( ) 3. ( ) What do I need to know? o The Cartesian coordinate system is made up of two perpendicular number lines called the x-axis (horizontal)) and the y-axis (vertical). o The point of intersection between the axes is called the origin. o Points, or ordered pairs, are given by their distance from zero along each axis in the form: ( ) B. Determine whether an ordered pair is a solution to a linear equation. What does a problem look like? Is ( ) a solution to the equation ? Answer: No. What do I need to know? o If an ordered pair is a solution to a linear equation the x and y values can be substituted to make a true statement. o “A graph of an equation in two variables is an illustration of the set of points whose coordinates satisfy [are solutions of] the equation.” – page 407 Page 1 of 3 MATH 0960 7.1 Notes o “A set of points that are on a line are said to be collinear.” – page 407 Example: Determine whether the three points appear to be collinear. ) 1. ( ) ( ) ( 2. ( 3. ( )( ( ) )( ) ) ( ) Page 2 of 3 MATH 0960 7.1 Notes C. Solve applications. What does a problem look like? Example: The graph to the right depicts cost vs. mileage for two rental companies: U-Move and Bargain. Use the graph to answer questions below. Rental Cost 45 U-Move Bargain 40 35 Cost (USD) 30 25 20 15 10 5 0 0 10 20 30 40 50 60 70 Mileage 80 90 100 110 120 1. Find the ordered pair representing the point at which the lines cross. This represents the mileage and cost for when the two companies charge the same amount. Answer: ( ) 2. What is the base price of each rental, that is, what is the cost if the mileage is zero? Answer: U-Move is $10, Bargain is $20 3. How much does each rental cost if 120 miles are driven? Answer: U-Move costs $40, Bargain costs $38 Page 3 of 3