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Rewrite the following equation in standard form.\newliney=7x+9y = 7x + 9\newlineHint: The standard form of a linear equation is Ax+By=CAx + By = C where AA and BB are not both zero, and AA, BB, and CC are integers whose GCF is 11.

Full solution

Q. Rewrite the following equation in standard form.\newliney=7x+9y = 7x + 9\newlineHint: The standard form of a linear equation is Ax+By=CAx + By = C where AA and BB are not both zero, and AA, BB, and CC are integers whose GCF is 11.
  1. Given Equation: Start with the given equation.\newlineThe given equation is y=7x+9y = 7x + 9.\newlineWe need to rewrite this equation in standard form, which is Ax+By=CAx + By = C.
  2. Move x Term: Move the term with xx to the left side of the equation.\newlineTo do this, we subtract 7x7x from both sides of the equation.\newliney7x=7x+97xy - 7x = 7x + 9 - 7x\newlineThis simplifies to y7x=9y - 7x = 9.
  3. Rearrange to Standard Form: Rearrange the terms to match the standard form.\newlineThe standard form is Ax+By=CAx + By = C, so we need to write the xx term first.\newline7x+y=9-7x + y = 9
  4. Make X Coefficient Positive: Ensure that the coefficient of xx is positive.\newlineIf we multiply the entire equation by 1-1, we will get the xx coefficient to be positive.\newline(1)(7x)+(1)y=(1)9(-1)(-7x) + (-1)y = (-1)9\newlineThis simplifies to 7xy=97x - y = -9.
  5. Check Coefficients: Check if the coefficients are integers whose greatest common factor (GCF) is 11. The coefficients are 77, 1-1, and 9-9. The GCF of these numbers is 11.

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