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Converting Linear Equations to Standard Form

Learn how to convert linear equations from slope-intercept or point-slope form to standard form. Includes examples and practice problems.

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Converting Linear Equations to Standard Form

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  1. 5.6– Standard Form of a Linear Equation Goal: - Write a linear equation in standard form - Use the standard form of an equation to model a real life situation (that means a word problem). QUESTION: How do we define an integer?

  2. You will USUALLY have to transform FROM slope intercept or point slope form TO Standard Form. That just means that you will have to add or subtract to get the variables on the LEFT, the constant on the RIGHT. Be careful if you have coefficients or the constant term is NOT an integer. You WILL have to get rid of the fraction (but not necessarily by multiplying by the reciprocal!

  3. NOT  examples of linear equations instandard form x + y = 5 2x – 4y = 6 y = -1x -14 5x -15 = -2y 2 YES  examples of linear equations in standard form 7 5 x + 2y = 10 14x – 4y = 42 x + 5y = -70 5x + 2y = 15

  4. NOT  examples of linear equations instandard form • slope – intercept form • y = mx + b • point-slope form • y – y1 = m(x – x1) • any fractions present YES  Examples of linear equations instandard form x & y together an integer alone all integers, no fractions easy to find intercepts used in comparing 2 different types of things

  5. Original Equation Get rid of the fraction Distribute Simplify Subtract 2x from each side Done! Example: Write in standard form with integer coefficients.

  6. Problem with Words in It You are in charge of buying the hamburger and boned chicken for a BBQ. The hamburger costs $2 per pound and the boned chicken costs $3 per pound. You have $30 to spend. a. Write an equation that models the different amounts of hamburger and chicken that you can buy. b. Make a table and a graph that illustrate several different amounts of hamburger and chicken that you can buy.

  7. Equations of Lines Slope Intercept Form: y = mx + b Point-Slope Form: y – y1 = m(x – x1) Vertical Line (undefined slope): x = x-intercept Horizontal Line (Zero Slope): y = y-intercept Standard Form (Define A, B, C): Ax + By = C

  8. Homework Complete worksheet!

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