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Graphing Linear Equations Verifying Solutions of an Equation a) Substitute the ordered pair into the equation b) Simplify both sides of the equation c) If the numbers are the same: the ordered pair is a solution If the numbers are different: the ordered pair is not a solution Examples 1) Is (1,2) a solution of x + 3y = 6? a) 1 + 3(2) = 6 b) 7 ≠ 6 c) Not a solution 2) Is (3,-1) a solution of y = 2x – 7? a) -1 = 2(3) – 7 b) -1 = -1 c) Solution Try these: Determine if the ordered pair is a solution 1) y =2x – 3 (-7, -1) 2) -4x + 3y = 1 (5,7) Graphing with Tables from Equations a) Rewrite the equation in the form y = mx + b (Solve for y) b) Choose four x-values for a table c) Plug in the x-values to find the corresponding y-values d) Plot your points and draw a line through them Examples Given: y + 2 = 3x a) y = 3x – 2 b&c) d) x y -1 -5 0 -2 1 1 2 4 62 Given: 2x – 2y = 6 a) -2y = -2x + 6 -2 -2 y=x–3 b&c) x -1 0 1 2 y -4 -3 -2 -1 Try these: 1) y – 1 = x x y d) 2) 4x + 2y = -6 x y 63 Special Equations Graph y = 4 This graph is a horizontal line and goes through 4 on the y axis Graph x = -3 This graph is a vertical line and goes through -3 on the x- axis Horizontal Lines have zero slopes Vertical lines have undefined slopes or “no slope” Try These: What is the equation? What is the equation? What is the slope? What is the slope? 64 Graphs Using x and y-intercepts x-intercept Example: The point where the graph crosses the x-axis To find the x-intercept: a) Substitute 0 for y b) Solve for x Given: 2x + 3y = 6 2x + 3(0) = 6 2x = 6 x=3 ________________________________________________________________________ y-intercept Example: Given y = 3x + 1 The point where the graph crosses the y-axis y = 3(0) + 1 To find the y-intercept: a) Substitute 0 for x y=1 b) Solve for y _______________________________________________________________________ Find the x and y-intercepts of the following: y = 2x – 4 Then graph it. x –intercept 0 = 2x – 4 y -intercept y = 2(0) – 4 4 = 2x y=0–4 2=x y = -4 Try These: Find the x and y intercept of each equation and graph the equation: 11) 3x + 5y = 15 12) y = x + 4 6) -2x + 4y = -8 x-intercept _________ y-intercept__________ x-intercept _________ y-intercept__________ x-intercept _________ y-intercept__________ 65 I. Determine if the ordered pair is a solution 1) y = 3x – 4 (-5, -11) 2) -6x + 5y = -6 3) 2x – 7y = -20 (-3, 2) 4) y = 12x – 4 5) 3x + 8y = -10 (-2, 7) 6) y = 4x – 10 (4,6) (-3, -32) (12, 38) II. Use the equation to make a table of 3 values, then graph the line 7) y = -3x + 2 8) y = 2x – 4 x y x y 66 9) y – 4 = -2x 10) -6x + 3y = -15 x x y y Find the x and y intercept of each equation and graph the equation: 11) 3x + 4y = 12 12) y = x + 2 13) 2x + 5y = 10 x-intercept _________ x-intercept _________ x-intercept _________ y-intercept__________ y-intercept__________ y-intercept__________ 67 Special Equations 14) What is the equation? 15)What is the equation? What is the slope? What is the slope? 16) What is the equation? 17)What is the equation? What is the slope? What is the slope? 68 I. Determine if the ordered pair is a solution 1) y = 3x – 4 (-5, -11) 2) -6x + 5y = -6 3) 4x – y = 1 (-1, 3) 4) 2y – 3x = 5 (4, 1) (4,6) 5) -5x + 10y = 20 (2, 3) II. Use the equation to make a table of 3 values, then graph the line 6) y = -3x + 2 7) y = 2x - 4 x -1 0 1 2 y x y Find the x and y intercept of each equation and graph the equation: 8) 3x + 4y = 12 9) y = x + 2 10) 2x + 5y = 10 x-intercept _________ x-intercept _________ x-intercept _________ y-intercept__________ y-intercept__________ y-intercept__________ 69 Practice Mini-Test Determine if the ordered pair is a solution 1) y = -5x + 7 (6, -23) Use the equation to make a table of 3 values, then graph the line 3) y = -x + 2 x y -1 0 1 2 2) -3x + 7y = -4 (4,2) Find the x and y intercept of each equation and graph the equation: 4) 6x – 3y = -12 x-intercept _________ y-intercept _________ 5) What is the equation of the line? 7) Graph the equation x = -4 6) What is the slope of the line? 8) What is the slope of the line? 70