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Standard and Slope-Intercept Forms

Standard and Slope-Intercept Forms. Standard Form: Ax + By = C Slope-Intercept Form: y = mx + b IMPORTANT: B ≠ b You can convert between standard and slope-intercept forms by performing inverse operations. Inverse Operations: Multiply Divide

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Standard and Slope-Intercept Forms

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  1. Standard and Slope-Intercept Forms

  2. Standard Form: Ax + By = C Slope-Intercept Form: y = mx + b IMPORTANT: B ≠ b You can convert between standard and slope-intercept forms by performing inverse operations. Inverse Operations: Multiply Divide Divide Multiply Add Subtract Subtract Add REMEMBER: Properties of Equality – what is done to one side of the equation must be done to the other side

  3. How do you convert from standard form to slope-intercept form? Ax + By = C y = mx + b (Solve for y) Example1: 6x + y = 12 (standard form) (1)Subtract 6x from each side -6x -6x y = -6x + 12 (slope-intercept form) m = ______ b = ______ Example 2: 10x + 5y = 25 (standard form) (1)Subtract 6x from each side -10x -10x (2) Divide by 5 on each side 5y = -10x + 25 5 5 y = -2x + 5 TRY THESE: Convert from standard form to slope-intercept form 1. 40x – 5y = -10 2. -10x + 2y = 30 3. x + y = -7 4. 2x – y = 12

  4. SOLUTIONS: 1. 40x – 5y = -10 2. -10x + 2y = 30 3. x + y = -7 4. 2x – y = 12 1) y = 8x + 2 • y = 5x + 15 • y = -x + (-7) or y = -x – 7 • y = 2x – 12

  5. How do you convert from slope-intercept form to standard form? y = mx + b Ax + By = C Example 1: y = 3x – 5 (slope-int form) (1) Subtract 3x from each side -3x -3x -3x + y = -5 (standard form) Example 2: y = 4 x + 12 (slope-int form) (1)Subtract 4 x from each side -4x -4x -4 x + y = 12 TRY THESE: Convert from slope-intercept form to standard form 1. y = 3 x – 15 3. y = -x – 1 2. y = -10x – 2 4. y = x

  6. SOLUTIONS: 1. y = 3 x – 15 3. y = -x – 1 2. y = -10x – 2 4. y = x 1) -3x + y = -15 • 10x + y = -2 • x + y = -1 • -x + y = 0

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