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

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”

Standard FormSlope-Intercept Form Ax + By = C y = mx + b 3x + 2y = 8 - 3x 2y = - 3x y = x 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

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

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

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

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

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

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

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

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

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

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