Transcript Lesson 20
Bell Quiz Objectives • Learn to graph on a coordinate plane. Coordinate Plane • A coordinate plane is made of two perpendicular number lines, one horizontal and one vertical. • The horizontal line is called the x-axis, and the vertical line is called the y-axis. • The number lines divide the pane into four quadrants. • The intersection of the x- and y-axis is called the origin. Coordinate Plane Coordinate Plane • Each point on the coordinate plane is identified by an ordered pair, or two numbers in parentheses, separated by a comma. • An ordered pair is written as follows: (x, y) • The ordered pair that represents the origin is (0,0). Coordinate Plane • The first number in an ordered pair is called the x-coordinate and indicates the distance to the right or left of the origin. • The second number, the y-coordinate, is the distance above or below the horizontal axis. Coordinate Plane • A coordinate is a number that helps locate a point on a graph. • To find or graph a point, always start at the origin. • Then use the sign of the coordinate to determine the location of the point. Coordinate Plane (–, +) (+, +) (–, +) (–, –) (+, –) Example 1 Graphing Ordered Pairs on a Coordinate Plane Graph the ordered pair: (4, 2) Example 2 Graphing Ordered Pairs on a Coordinate Plane Graph the ordered pair: (– 3, 0) Lesson Practice Graph each ordered pair on a coordinate plan. Label each point. a. (0, 5) d. (– 3, 4) b. (– 1, – 6) e. (5, – 1) c. (– 2, 0) f. (2, – 4) New Concepts • When there is a relationship between two variable quantities, one variable is the independent variable and the other is the dependent variable. Variables Independent Variable: The variable whose value can be chosen. Also called the input variable. Dependent Variable: The variable whose value is determined by the input value of another variable. Also called the output value. Example 3 Identify Independent and Dependent Variables For each pair of variables, identify the independent variable and the dependent variables. a. Number of traffic violation, cost of auto insurance. Example 3 Identify Independent and Dependent Variables For each pair of variables, identify the independent variable and the dependent variables. b. Electric bill total, kilowatts of electricity used. Lesson Practice For each pair of variables, identify the independent variable and the dependent variables. The amount paid, the number of items purchased. Lesson Practice For each pair of variables, identify the independent variable and the dependent variables. The number of hours worked, the number of yards mowed. New Concept • A solution to an equation with two variables is an ordered pair that makes the equation true. • There are infinite solution to the equation y = 4x + 2. • Solutions can be found by substituting values for the independent variable, x, to find the corresponding value of the dependent variable, y. Example 4 Determining the Dependent Variable Complete the table for the equation y = 4x + 2. x –2 0 2 ¾ y Lesson Practice Complete the table for the equation y = 2x – 1 x y –3 –2 –1 Example 5 Application: Wages The federal minimum wage is about $5 per hour. The total on a minimum wage worker’s paycheck is dependent on the number of hours worked. The paycheck total can be calculated using the equation y = 5x. Find the pay for 1, 3, 5, and 8 hours of. Make a graph to represent the equation. Lesson Practice The prom committee raises money for the prom by selling flowers. The money earned for the prom is dependent on the number of flowers sold. Money earned is represented by the equation y = 3x – 75. Find the amount of money raised when 25, 50, 75, and 100 flowers are sold. Make a graph to represent the equation.