1. Ch 5.4 Objective: To rewrite an equation between standard form and slope-intercept form and graph it.

2. Definitions & Steps for solving Standard FormSlope-Intercept Form Ax + By = Cy = mx + b 1)Subtract “Ax” from both sides 2)Divide both sides by “B”

3. Standard FormSlope-Intercept Form Ax + By = C y = mx + b 3x + 2y = 8 - 3x 2y = - 3x + 8 2 2 2 y = x + 4 -3-3 2 y = x -3 2 To change Standard Form to Slope-Intercept Form just solve the equation for y. Example 1: Write 3x + 2y = 8 in slope-intercept form. + 4 To graph: Go up 4 units from origin (0,0) then “rise” -3 units and “run” 2 units } down 3 units

4. Example 2: Graph the following equation. - 4x + 3y = 6 +4x 3y = 4x + 6 3 3 3 y = x + 2 4 3 x y +4+4 +3+3

5. Example 3: Graph the following equation. 2x + 6y = 3 - 2x 6y = - 2x + 3 6 y = x + -2-2 6 3 6 -1 3 m = -1 3 b = x y -1 +3+3 1 2 1 2

6. Example 4: Graph the following equation. y = x + 0 x y +1+1 +1+1 - x + y = 0 + x b = 0 m = 1

7. Convert the following linear equation to standard form. Not in standard form ! Ax + By = C y = 2x + 5 -2x -2x + y = 5 or2x - y = -5

8. Convert the following linear equation to standard form. Not in standard form ! Ax + By = C Where A, B and C are integers. -x + 2y = -2or x - 2y = 2

9. Convert the following linear equation to standard form. Not in standard form ! Ax + By = C Where A, B and C are integers. 2x + 3y = 21

10. Convert the following linear equation to standard form. Not in standard form ! Ax + By = C Where A, B and C are integers. 3y = 5x - 12 -5x -5x + 3y = -12 or5x - 3y = 12

11. Convert the following linear equation to standard form. Not in standard form ! Ax + By = C Where A, B and C are integers. 5y = -3x - 40 +3x 3x + 5y = -40

12. - x + y = 4 - x Write a linear equation in standard form given: slope = y-intercept = 4 2 3 y = mx + b y = x + 4 2 3 Not in standard form ! Ax + By = C Where A, B and C are integers. 2 3 2 3 2 3 2 3 No fractional coefficients! 3 - 2x + 3y = 12 or 2x - 3y = - 12

13. - x + y = -1 - x Write a linear equation in standard form given: slope = y-intercept = -1 5 4 y = mx + b y = x - 1 5 4 Not in standard form ! Ax + By = C Where A, B and C are integers. 5 4 5 4 5 4 5 4 No fractional coefficients! 4 - 5x + 4y = -4 or 5x - 4y = 4