Write Linear Equations In Standard Form Worksheet

6 problems

To write standard form for linear equations is \(Ax + By = C \), where both \(A \) and \(B \) are non-zero integers and \(A \), \(B \), and \(C \) are integers. \( A \) is usually a positive integer. This form can be transformed to slope-intercept form for simpler graphing and behavior interpretation, and it is helpful for evaluating linear relationships.

Algebra 1
Linear Relationship

How Will This Worksheet on "Write Linear Equations in Standard Form" Benefit Your Student's Learning?

  • Rearranging equations is a practice that improves algebraic competence.
  • Aids in understanding how lines and their attributes are represented in equations.
  • Utilizes multiple step equation problems to foster critical thinking.
  • Shows how to use linear equations in real-world situations.
  • Establishes a solid basis for more complex mathematical ideas.
  • Consistent practice helps build self-confidence in solving and interpreting equations.

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Solved Example

Q. Determine the standard form of the following equation:\newliney=7x+4y = 7x + 4
Solution:
  1. Rearrange equation for standard form: To rewrite the equation y=7x+4y = 7x + 4 in standard form, we need to rearrange the terms so that the xx and yy terms are on one side of the equation and the constant is on the other side. We want it in the form Ax+By=CAx + By = C.
  2. Subtract xx term from both sides: The given equation is y=7x+4y = 7x + 4. To get it into standard form, we need to subtract 7x7x from both sides of the equation to move the xx term to the left side.
  3. Adjust xx coefficient to be positive: Subtracting 7x7x from both sides gives us 7x+y=4-7x + y = 4. This is almost in standard form, but we typically want the xx coefficient to be positive.
  4. Multiply equation by 1-1: To make the xx coefficient positive, we can multiply the entire equation by 1-1. This gives us 7xy=47x - y = -4.
  5. Check coefficients for GCF: Now the equation is in standard form, Ax+By=CAx + By = C, with A=7A = 7, B=1B = -1, and C=4C = -4. We need to check that AA, BB, and CC are integers whose greatest common factor (GCF) is 11.
  6. Verify standard form : The GCF of 77, 1-1, and 4-4 is indeed 11, so the equation is in standard form where A and B are not both zero, and A, B, and C are integers whose GCF is 1. .

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