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Ch 7 Graphs and Linear Equations Review on Graphing Ordered Pair y 8 6 (x, y) 4 2 -10 -5 “origin” (0,0) 5 -2 -4 -6 Coordinate Plane -8 10 x Ordered Pair y 8 6 (5, 4) 4 2 -10 -5 “origin” (0,0) 5 -2 -4 -6 Coordinate Plane -8 10 x Ordered Pair y 8 6 (5, -4) 4 2 -10 -5 “origin” (0,0) 5 -2 -4 -6 Coordinate Plane -8 10 x Ordered Pair y 8 6 (-5, -4) 4 2 -10 -5 5 -2 -4 -6 Coordinate Plane -8 10 x Ordered Pair y 8 6 (-5, 0) 4 2 -10 -5 (-5,0) 5 -2 -4 -6 Coordinates -8 10 x Graph (0, 6) y 8 6 second quadrant -10 4 2 -5 third quadrant (0,6)first quadrant 5 -2 -4 fourth quadrant Not in a quadrant quadrants if on either axis -6 -8 10 x What are the coordinates? Which quadrant? y 8 6 4 2 (1,1) -10 -5 5 -2 -4 -6 -8 10 x y 8 6 4 (-3, 3) -10 What are the coordinates? Which quadrant? 2 -5 5 -2 -4 -6 -8 10 x y 8 6 4 What are the coordinates? Which quadrant? 2 -10 -5 5 -2 -4 -6 -8 (5, -2) 10 x y 8 6 4 What are the coordinates? Which quadrant? 2 -10 -5 5 -2 (0, -5) -4 -6 Not in a quadrant if on either axis -8 10 x 7.2 Graphing Equations Determine if the ordered pair is a solution of the equation. y = 2x + 1 (3 , 7 ) 7 = 2(3) + 1 YES The ordered pair (3,7) is a solution. Determine if the ordered pair is a solution of the equation. 4y - 3x = 22 (-2 , 4 ) 4(4) – 3 (-2)= 22 16 + 6 = 22 YES The ordered pair (-2,4) is a solution. Determine if the ordered pair is a solution of the equation. y - 3x = -2 (-2 , 8 ) (8) – 3 (-2)= -2 ??? 8 + 6 -2 NO The ordered pair (-2,8) is not a solution. Graphing Equations • Make a Table Making a Table 1. Solve the equation in y = format (slope intercept form) 2. Pick your x values (-1, 0,1) unless slope is a fraction and y-intercept is not 3. Plug in the x values into x in the equation to find the corresponding y values 4. Plot the (x, y) ordered pairs on the coordinate plane Graph: y=x y 8 x y 6 4 2 -10 -5 5 -2 -4 -6 -8 10 x y Find 3 solutions 8 6 y = 2x + 1 4 2 -10 -5 5 10 x X Values Y=2x + 1 Y Values (x,y) 1 2(1) +1 3 (1,3) 2(0) +1 1 (0,1) -2 -4 -6 0 -8 -1 2(-1) +1 -1 (-1,-1) Solve for ‘y’ 9 x 3y 20 9x 9x 3y 9 x 20 3 3 3 20 y 3x 3 Solve for ‘y’ means “get y all by itself” y Graph: 8 -2x + y = 5 y = 2x + 5 6 4 2 -10 -5 5 X Y=2x +5 10 Y (x,y) x -2 1 2(1) +5 7 (1,7) 0 2(0) +5 5 (0,5) -4 -6 -1 2(-1)+5 3 (-1,3) -8 Graph: y -2x + 3y = 15 8 3y = 2x + 15 2 x 15 y 3 -10 6 4 2 -5 Y=2/3x +5 x Y=2/3x +5 5 10 y x (x,y) -2 7 (3,7) 3 (2/3)(3) +5 0 (2/3) (0) +5 5 (0,5) -3 (2/3)(-3)+5 3 (-3,3) -4 -6 -8 Graph: 3x - y = 2 3x = y + 2 3x - 2 = y y 8 x y 6 4 2 -10 -5 5 -2 -4 -6 -8 10 x •Assignment: Page 311 (2-26 even, 28-31 all) -