Linear Functions Forms of Linear Equations Standard Form

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Linear Functions Forms of Linear Equations Standard Form

Linear Functions Forms of Linear Equations Standard Form

Linear Functions Forms of linear equations Information and Definitions Order Pair Notations: (x, y)

Linear Functions Forms of linear equations Information and Definitions Order Pair Notations: (x, y) more than one point (x 1, y 1), (x 2, y 2), (x 3, y 3), …(xn, yn) Variable representation: m = slope, constant rate of change, gradient, and the following: rise change in y delta y ∆y run change in x delta x ∆x b = y-intercept, (0, y) x-intercept = (x, 0) A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero

Linear Functions Forms of linear equations Information and Definitions Standard Form: Ax + By

Linear Functions Forms of linear equations Information and Definitions Standard Form: Ax + By = C 3 x + 4 y = 17; Graph using the x and y intercepts x-intercept = (17/3 , 0) ; y-intercept = (0, 17/4) Slope Intercept Form: y = mx + b y = 3 x + 5; Graph using the y-intercept and the slope b = 5; m = 3 Point Slope Form: y - y 1 = m(x - x 1) y - 4 = 3(x -5); Graph using the point and the gradient point = (5, 4); m = 3 Slope equation: m = y 2 - y 1 x 2 - x 1

Forms of linear equations Standard Form: Ax + By = C Write in Standard

Forms of linear equations Standard Form: Ax + By = C Write in Standard Form Given A, B, C A= 3; B=1; C=12 Standard Form Ax + By = C 3 x + 1 y = 12 A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero. Find x and y intercepts Standard Form: Ax + By = C 3 x + y = 12 x-intercept y = 0 3 x + 0 = 12 3 x = 12 x=4 (4, 0) x-intercept y-intercept x = 0 3(0) + y = 12 y=12 (0, 12) y-intercept x-intercept = (4, 0) y-intercept = (0, 12)

Forms of linear equations Standard Form: Ax + By = C Write in Standard

Forms of linear equations Standard Form: Ax + By = C Write in Standard Form Given A, B, C A= 3; B=1; C=12 Standard Form Ax + By = C 3 x + 1 y = 12 A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero. Graph Ax + Bx = C Standard Form: Ax + By = C 3 x + y = 12 Graph using the x-intercept and y-intercept x-intercept = (12/3 , 0) = (4, 0) y-intercept = (0, 12/1) = (0, 12) 3 x + y = 12

Forms of linear equations Standard Form: Ax + By = C Write in Standard

Forms of linear equations Standard Form: Ax + By = C Write in Standard Form Given Any Linear Equation 4 x = -3 y -3 Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below * 4 x = -3 y -3 4 x + 3 y = -3 Identify A, B, C: Original equation Add 3 y to both sides A=4; B=3; C=-3 Satisfies the criteria* below *A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero. Find x and y intercepts Standard Form: Ax + By = C 4 x + 3 y = -3 x-intercept y = 0 y-intercept x = 0 4 x + 3(0) = -3 4(0) + 3 y = -3 4 x = -3 3 y = -3 x = -¾ = -. 75 y=-3/1 = -1 (-. 75, 0) (0, -1) x-intercept y-intercept x-intercept = (-. 75, 0) y-intercept = (0, -1)

Forms of linear equations Standard Form: Ax + By = C Write in Standard

Forms of linear equations Standard Form: Ax + By = C Write in Standard Form Given Any Linear Equation 4 x = -3 y -3 Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below * 4 x = -3 y -3 4 x + 3 y = -3 Identify A, B, C: Original equation Add 3 y to both sides A=4; B=3; C=-3 Satisfies the criteria* below *A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero. Graph Ax + Bx = C Standard Form: Ax + By = C 4 x + 3 y = -3 Graph using the x and y intercepts x-intercept = (-3/4 , 0) = (-. 75, 0) y-intercept = (0, -3/3) = (0, -1)

Forms of linear equations Standard Form: Ax + By = C Write in Standard

Forms of linear equations Standard Form: Ax + By = C Write in Standard Form Given Slope Intercept Form y = 7 x + 3 Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below * y = 7 x + 3 -7 x + y = 3 Original equation Subtract 7 x from both sides(A is not >= 0) 7 x - y = -3 Multiply both sides by -1 Identify A, B, C: A=7; B=-1; C=-3 Satisfies the criteria* below *A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero. Find x and y intercepts Standard Form: Ax + By = C 7 x - y = -3 x-intercept y = 0 7 x - 0 = -3 7 x = -3/7 (-3/7, 0) x-intercept y-intercept x = 0 7(0) - y = -3 -y = -3 y=3 (0, 3) y-intercept x-intercept = (-3/7 , 0) y-intercept = (0, 3)

Forms of linear equations Standard Form: Ax + By = C Write in Standard

Forms of linear equations Standard Form: Ax + By = C Write in Standard Form Given Slope Intercept Form y = 7 x + 3 Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below * y = 7 x + 3 -7 x + y = 3 Original equation Subtract 7 x from both sides(A is not >= 0) 7 x - y = -3 Multiply both sides by -1 Identify A, B, C: A=7; B=-1; C=-3 Satisfies the criteria* below *A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero. Graph Ax + Bx = C Standard Form: Ax + By = C 7 x - y = -3 Graph using the x and y intercepts x-intercept =(-3/7, 0) y-intercept = (0, 3)

Forms of linear equations Standard Form: Ax + By = C Write in Standard

Forms of linear equations Standard Form: Ax + By = C Write in Standard Form Given Slope Intercept Form y = -4/9 x + 6 Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below * y = -4/9 x + 6 4/9 x + y = 6 Original equation Add 4/9 x to both sides(A is not an Integer) 4 x + 9 y = 54 Identify A, B, C: Multiply both sides by 9 Find x and y intercepts Standard Form: Ax + By = C 4 x + 9 y = 54 x-intercept y = 0 y-intercept x = 0 4 x + 9(0) = 54 4(0) + 9 y = 54 4 x = 54 9 y = 54 x = 54/4 = 13. 5 y = 54/9 = 6 (13. 5, 0) (0, 6) x-intercept y-intercept A=4; B=9; C=54 Satisfies the criteria* below *A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero. x-intercept = (13. 5, 0) y-intercept = (0, 6)

Forms of linear equations Standard Form: Ax + By = C Write in Standard

Forms of linear equations Standard Form: Ax + By = C Write in Standard Form Given Slope Intercept Form y = -4/9 x + 6 Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below * y = -4/9 x + 6 4/9 x + y = 6 Original equation Add 4/9 x to both sides(A is not an Integer) 4 x + 9 y = 54 Identify A, B, C: Multiply both sides by 9 A=4; B=9; C=54 Satisfies the criteria* below *A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero. Graph Ax + Bx = C Standard Form: Ax + By = C 4 x + 9 y = 54 Graph using the x and y intercepts x-intercept = (54/4 , 0) = (13. 5, 0) y-intercept = (0, 54/9) = (0, 6)

Linear Functions Forms of linear equations Information and Definitions Order Pair Notations: (x, y)

Linear Functions Forms of linear equations Information and Definitions Order Pair Notations: (x, y) more than one point (x 1, y 1), (x 2, y 2), (x 3, y 3), …(xn, yn) Variable representation: m = slope, constant rate of change, gradient, and the following: rise change in y delta y ∆y run change in x delta x ∆x b = y-intercept, (0, y) x-intercept = (x, 0) A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero

Linear Functions Forms of linear equations Information and Definitions Standard Form: Ax + By

Linear Functions Forms of linear equations Information and Definitions Standard Form: Ax + By = C 3 x + 4 y = 17; Graph using the x and y intercepts x-intercept = (17/3 , 0) ; y-intercept = (0, 17/4) Slope Intercept Form: y = mx + b y = 3 x + 5; Graph using the y-intercept and the slope b = 5; m = 3 Point Slope Form: y - y 1 = m(x - x 1) y - 4 = 3(x -5); Graph using the point and the gradient point = (5, 4); m = 3 Slope equation: m = y 2 - y 1 x 2 - x 1

Linear Functions Forms of Linear Equations Standard Form

Linear Functions Forms of Linear Equations Standard Form

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