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Converting Linear Equations: Standard to Slope-Intercept Form

Learn how to convert linear equations from standard form to slope-intercept form. Practice converting equations and identifying slope and y-intercept.

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Converting Linear Equations: Standard to Slope-Intercept Form

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  1. Warm ups Volunteers to the board!!  Graph using intercepts: 1) 2x + 3y = 12 2) 4x – 5y = 20 3) 2x – y = -4

  2. Convert Standard to Slope-Intercept Objective: To convert a linear equation from standard form to slope-intercept form.

  3. -2/3 What is the slope of #1? _____ • Part of being able to analyze a graph is being able to say the slope. • Also, sometimes it is easier to graph with the slope and y-intercept than with the x-and y-intercept. • Writing an equation from a graph is easier to do with slope and y intercept (y = mx + b) • You will have to do this on your test!

  4. Convert StandardSlope-Intercept Steps: 1. Subtract Ax 2. Divide everything by B y = mx + b Ax + By = C

  5. Example 1 Convert the equation from standard form to slope-intercept form: 2x + 3y = 12 -2x -2x 3y = -2x + 12 3 3 3 y = -2x + 4 3 Steps: • Subtract Ax • Divide everything by B Ax + By = C

  6. Example 2 Convert the equation from standard form to slope-intercept form: 2x – y = -4 -2x -2x -y = -2x – 4 -1 -1 -1 y = 2x + 4 Steps: • Subtract Ax • Divide everything by B Ax + By = C

  7. Convert to slope-intercept form: 4x – 5y = 10 Now, identify the slope and y-intercept: (hint: slope is m, y-intercept is b) Slope:______ y-intercept:_______ y = 4/5x – 2 4/5 -2

  8. In General Ax + By = C y = -a x + c b b m = -a/b y-intercept = c/b

  9. Identify slope and y-intercept: 5x + 2y = 12 -5x -5x 2y = -5x + 12 2 2 2 y = -5/2x + 6 Slope:______ y-intercept:_______ y = -5/2x + 6 -5/2 6

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