1. Linear Functions Forms of Linear Equations Standard Form

2. 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 ), …(x n, y n ) Variable representation: m = slope, constant rate of change, gradient, and the following: risechange in ydelta y∆ y runchange in xdelta 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

3. Linear Functions Forms of linear equations Information and Definitions Standard Form: Ax + By = C 3x + 4y = 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 = 3x + 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

4. 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 3x + 1y = 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 3x + y = 12 x-intercept y = 0y-intercept x = 0 3x + 0 = 123(0) + y = 12 3x = 12 x = 4y=12 (4,0)(0,12) x-intercepty-intercept x-intercept = (4, 0) y-intercept = (0, 12)

5. 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 3x + 1y = 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 3x + y = 12 Graph using the x-intercept and y-intercept x-intercept = (12/3, 0) = (4, 0) y-intercept = (0, 12/1) = (0, 12) 3x + y = 12

6. Forms of linear equations Standard Form: Ax + By = C Write in Standard Form Given Any Linear Equation 4x = -3y -3 Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below * 4x = -3y -3 Original equation 4x + 3y = -3 Add 3y to both sides Identify A, B, C: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 4x + 3y = -3 x-intercept y = 0y-intercept x = 0 4x + 3(0) = -34(0) + 3y = -3 4x = -3 3y = -3 x = -¾ = -.75 y=-3/1 = -1 (-.75,0) (0,-1) x-intercepty-intercept x-intercept = (-.75, 0) y-intercept = (0, -1)

7. Forms of linear equations Standard Form: Ax + By = C Write in Standard Form Given Any Linear Equation 4x = -3y -3 Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below * 4x = -3y -3 Original equation 4x + 3y = -3 Add 3y to both sides Identify A, B, C: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 4x + 3y = -3 Graph using the x and y intercepts x-intercept = (-3/4, 0) = (-.75, 0) y-intercept = (0, -3/3) = (0, -1)

8. Forms of linear equations Standard Form: Ax + By = C Write in Standard Form Given Slope Intercept Form y = 7x + 3 Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below * y = 7x + 3 Original equation -7x + y = 3 Subtract 7x from both sides(A is not >= 0) 7x - 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 7x - y = -3 x-intercept y = 0y-intercept x = 0 7x - 0 = -37(0) - y = -3 7x = -3 -y = -3 x = -3/7 y = 3 (-3/7,0) (0,3) x-intercepty-intercept x-intercept = (-3/7, 0) y-intercept = (0, 3)

9. Forms of linear equations Standard Form: Ax + By = C Write in Standard Form Given Slope Intercept Form y = 7x + 3 Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below * y = 7x + 3 Original equation -7x + y = 3 Subtract 7x from both sides(A is not >= 0) 7x - 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 7x - y = -3 Graph using the x and y intercepts x-intercept =(-3/7, 0) y-intercept = (0, 3)

10. Forms of linear equations Standard Form: Ax + By = C Write in Standard Form Given Slope Intercept Form y = -4/9x + 6 Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below * y = -4/9x + 6 Original equation 4/9x + y = 6 Add 4/9x to both sides(A is not an Integer) 4x + 9y = 54 Multiply both sides by 9 Identify A, B, C: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. Find x and y intercepts Standard Form: Ax + By = C 4x + 9y = 54 x-intercept y = 0y-intercept x = 0 4x + 9(0) = 544(0) + 9y = 54 4x = 54 9y = 54 x = 54/4 = 13.5 y = 54/9 = 6 (13.5,0) (0,6) x-intercepty-intercept x-intercept = (13.5, 0) y-intercept = (0, 6)

11. Forms of linear equations Standard Form: Ax + By = C Write in Standard Form Given Slope Intercept Form y = -4/9x + 6 Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below * y = -4/9x + 6 Original equation 4/9x + y = 6 Add 4/9x to both sides(A is not an Integer) 4x + 9y = 54 Multiply both sides by 9 Identify A, B, C: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 4x + 9y = 54 Graph using the x and y intercepts x-intercept = (54/4, 0) = (13.5, 0) y-intercept = (0, 54/9) = (0, 6)

12. 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 ), …(x n, y n ) Variable representation: m = slope, constant rate of change, gradient, and the following: risechange in ydelta y∆ y runchange in xdelta 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

13. Linear Functions Forms of linear equations Information and Definitions Standard Form: Ax + By = C 3x + 4y = 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 = 3x + 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

14. Linear Functions Forms of Linear Equations Standard Form