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Rewrite the following equation in standard form.\newliney=4x+9y = 4x + 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=4x+9y = 4x + 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. Rewrite in Standard Form: To rewrite the equation y=4x+9y = 4x + 9 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. Move 4x4x Term: The given equation is y=4x+9y = 4x + 9. To move the term 4x4x to the other side of the equation, we can subtract 4x4x from both sides. This gives us 4x+y=9-4x + y = 9.
  3. Check Coefficients: We need to check if the coefficients AA, BB, and CC are integers whose greatest common factor (GCF) is 11. In this case, the coefficients are 4-4, 11, and 99. The GCF of these numbers is 11, so we do not need to divide the entire equation by any number to reduce the coefficients.
  4. Make Coefficient Positive: Finally, we should check if the coefficient AA is positive. The standard form prefers the coefficient of xx to be positive. Since our coefficient for xx is currently 4-4, we should multiply the entire equation by 1-1 to make it positive. This gives us 4xy=94x - y = -9.

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