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9/2/2009 Vocabulary Linear Equations in Two Variables Objectives: To determine if a given ordered pair is a solution, to define the coordinate plane and plot ordered pairs. Vocabulary (continued) Ordered pair – identifies the location of a point Coordinates – the numbers of a point on graph; p ; in the form ((x,y) ,y) the g x-coordinate – tells how far to move right (positive) or left (negative) from the origin; always first in an ordered pair y-coordinate –tells how far to move up (positive) or down (negative); always second in an ordered pair Example Complete the given ordered pairs. a) 3x – y = 5 (0, ___), (1, ___), ( ___, 5) coordinate plane – an area defined by two axes (number lines) that intersect at right angles x-axis – the horizontal (left to right) number liline y-axis – the vertical (up and down) number line origin – point where the axes intersect quadrants – the four regions of the coordinate plane Vocabulary (continued) solution -- an ordered pair (x,y) that “works” in the equation To complete a solution: Substitute the given x or y value into the equation and solve for the remaining variable. Example - Solution Complete the given ordered pairs. a) 3x – y = 5 (0, -5), (1, -2), (10/3, 5) 3(0) – y = 5 3(1) - y=5 3x – 5 = 5 -y = 5 3–y=5 3x = 10 y = -5 -y = 2 x = 10/3 (0, -5) y = -2 (10/3, 5) (1, -2) 1 9/2/2009 Example Example - Solution b) Complete the table for the equation y = -5x. b) Complete the table for the x y 3 0 -2 -20 Example Find the solution set for each equation given the replacement set by substituting for x and y. c) {(-5,0), (-3,-2), (2,13)} for y = 7 + 3x. Recognizing Ordered Pairs Name the coordinates of each point in the graph. d P d. Q W P V e. T f. Q g. W T h. V equation y = -5x. We must substitute each given value and find the other value. y=-5(3) = -15 0 = -5(x) 0=x y=-5(-2) = 10 -20=-5x 4=x x y 3 -15 0 0 -2 10 4 -20 Example - Solution Find the solution set for each equation given the replacement set by substituting for x and y. c) {(-5,0), (-3,-2), (2,13)} for y = 7 + 3x. We must substitute each given ordered pair to find which ones work or give us true statements. “work” (-5,0) Æ 0 = 7 + 3(-5) (-3,-2) Æ -2 = 7 + 3(-3) 0 = 7 – 15 -2 = 7 - 9 0 = -8 (false) -2 = -2 (true) (2,13) Æ 13 = 7 + 3(2) 13 = 7 + 6 So the solution set is (-3,-2) 13 = 13 (true) and (2, 13). Recognizing Ordered Pairs Solution Name the coordinates of each point in the graph. d P (-4,2) d. ( 4 2) Q W P V e. T (3,-2) f. Q (0,3) g. W (4,2) T h. V (-1,2) 2 9/2/2009 QUADRANTS in the Coordinate Plane Plotting Points y 5 II ((-,+) +) I (+ +) (+,+) 1. Start at the origin. 2. The first number tells you how much x III (-,-) IV (+,-) -5 (x,y) -5 to move left or right on the horizontal number line. 3. From there, the second number tells you how much to move up or down. 4. Draw a dot & label it. 5 Examples Examples - Solutions Plot each point. In which quadrant or on which axis would you find each point? 5 i) (-4, 2) Plot each point. In which quadrant or on which axis would you find each point? 5 i) (-4, 2) y y i j) (3, -2) j) (3, -2) l x k) (0, -5) l) (-3, 0) x j k) (0, -5) -5 -5 5 l) (-3, 0) -5 -5 k 5 3