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In this lesson we will write linear equations in standard form

In this lesson we will write linear equations in standard form. This equation is in slope-intercept form:. y = - ½ x + 6. This equation can be re-arranged another way so that x and y are together, and the fraction is eliminated.

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In this lesson we will write linear equations in standard form

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  1. In this lesson we will write linear equations in standard form

  2. This equation is in slope-intercept form: y = - ½ x + 6 This equation can be re-arranged another way so that x and y are together, and the fraction is eliminated.

  3. To put x and y on the same side of the equation, we can add ½x to both sides. y = - ½ x + 6 ½x + y = 6 What number would be multiplied by both sides to eliminate the fraction?

  4. To eliminate the fraction, we multiply each side of the equation by 2 y = - ½x + 6 2[½x + y] = [6]2 x + 2y = 12

  5. Now x and y are on the left side of the equation, and the fraction has been eliminated x + 2y = 12 Linear Equations that follow this pattern are in standard form. Ax + By = C

  6. Let’s write another equation in standard form: y = ¾x + 2 Both x and y should be on the left side of the equation in standard form. What should be done first?

  7. ¾x should be subtracted from both sides to ‘move’ the x to the left side of the equation y = ¾x + 2 - ¾x + y = 2 An equation in standard form contains no fractions or decimals. How can we eliminate the fraction in this equation?

  8. Multiply by 4 to eliminate the fraction - ¾x + y = 2 4[- ¾x + y] = [2]4 -3x + 4y = 8

  9. Since the equation has a negative in the first term, it can be eliminated by multiplying both sides of the equation by -1 -3x + 4y = 8 -1[-3x + 4y] = -1[8] 3x – 4y = -8 This step isn’t required, but on a multiple choice exam, you would need to perform this extra step if you don’t find the first equation.

  10. Write this equation in standard form How do we ‘move’ x to the left side?

  11. Add the term containing x to both sides (since it is negative)

  12. Eliminate the fraction

  13. Write this equation in standard form y = -2.5x – 3 Add 2.5x to both sides

  14. Write this equation in standard form y = -2.5x – 3 2.5x + y = -3 Now eliminate the decimal

  15. Multiply by 10 to remove the decimal 2.5x + y = -3 10[2.5x + y] = [-3]10 25x + 10y = -30 Let’s graph this equation using x and y intercepts

  16. Use zeros in the table to find x and y intercepts 25x + 10y = -30

  17. Graph the two pointsand connect 25x + 10y = -30

  18. Complete Activity 5c • Write equations in standard form and slope-intercept form • Graph equations in standard form and slope-intercept form • Identify equations in standard form and slope-intercept form

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