Math Problem Statement

y=(-2/3)x-(5/6) standard form

Solution

To convert the equation y=(23)x56y = \left(-\frac{2}{3}\right)x - \frac{5}{6} into standard form, we need to rewrite it in the form:

Ax+By=CAx + By = C

Where AA, BB, and CC are integers, and AA is positive.

Steps:

  1. Eliminate the fraction: To remove the fractions, multiply the entire equation by 6, which is the least common denominator of 3 and 6.

    6y=6(23x)6(56)6y = 6 \left(-\frac{2}{3}x\right) - 6\left(\frac{5}{6}\right)

    Simplifying:

    6y=4x56y = -4x - 5

  2. Rearrange the terms: Move all terms to one side of the equation to get the standard form:

    4x+6y=54x + 6y = -5

So, the standard form of the equation is:

4x+6y=54x + 6y = -5

Would you like any additional details on how to transform equations or solve them?

Related Questions:

  1. How do you find the slope of a line from standard form?
  2. How do you convert from standard form back to slope-intercept form?
  3. What does the constant term in standard form represent?
  4. How can you graph a line given its standard form equation?
  5. How do you determine if two lines are parallel or perpendicular?

Tip:

Always clear fractions by multiplying through by the least common denominator before converting to standard form.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Standard Form
Algebra

Formulas

Ax + By = C

Theorems

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Suitable Grade Level

Grades 8-10