Rewrite the following equation in standard form.y=9x+5Hint: The standard form of a linear equation is Ax+By=C where A and B are not both zero, and A, B, and C are integers whose GCF is 1.
Q. Rewrite the following equation in standard form.y=9x+5Hint: The standard form of a linear equation is Ax+By=C where A and B are not both zero, and A, B, and C are integers whose GCF is 1.
Identify Equation: Identify the given equation and the standard form requirement.The given equation is y=9x+5. We need to rewrite it in the standard form Ax+By=C, where A, B, and C are integers with a greatest common factor (GCF) of 1, and A should be non-negative.
Rearrange Terms: Rearrange the equation to get terms involving x and y on one side and the constant on the other side.To do this, we will subtract 9x from both sides of the equation to move the term involving x to the left side.y−9x=5−9xThis simplifies to:−9x+y=5
Ensure Non-Negative Coefficient: Ensure that the coefficient of x is non-negative.The standard form prefers the coefficient of x to be positive. To achieve this, we can multiply the entire equation by −1.−1(−9x+y)=−1(5)This simplifies to:9x−y=−5
Check GCF of Coefficients: Check if the coefficients have a GCF other than 1. The coefficients are 9, −1, and −5. The GCF of these numbers is 1.
Write Final Equation: Write the final equation in standard form.The equation in standard form is:9x−y=−5
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