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Equivalent Equations in Standard Form

Learn how to write equivalent equations in standard form and how to convert equations from point-slope form to standard form.

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Equivalent Equations in Standard Form

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  1. EXAMPLE 1 Write equivalent equations in standard form Write two equations in standard form that are equivalent to 2x – 6y =4. SOLUTION To write another equivalent equation, multiply each side by 0.5. To write one equivalent equation, multiply each side by 2. 4x – 12y =8 x – 3y = 2

  2. 1 – (–2) m= –3 = = 1 – 2 3 –1 Write an equation from a graph EXAMPLE 2 Write an equation in standard form of the line shown. SOLUTION STEP1 Calculate the slope. STEP2 Write an equation in point-slope form. Use (1, 1). y –y1=m(x –x1) Write point-slope form. y –1=–3(x –1) Substitute 1 for y1, 3 for m and 1 for x1.

  3. Write an equation from a graph EXAMPLE 2 STEP3 Rewrite the equation in standard form. 3x + y = 4 Simplify. Collect variable terms on one side, constants on the other.

  4. 1. Write two equations in standard form that are equivalent to x – y =3. ANSWER 2x – 2y =6, 3x – 3y = 9 EXAMPLE 1 for Examples 1 and 2 GUIDED PRACTICE

  5. 2. Write an equation in standard form of the line through (3, –1) and (2, –3). ANSWER –2x + y = –7 Write an equation from a graph EXAMPLE 2 for Examples 1 and 2 GUIDED PRACTICE

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