Rewrite the following equation in standard form.y=3x+8Hint: 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=3x+8Hint: 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 & Requirement: Identify the given equation and the standard form requirement.The given equation is y=3x+8. 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.
Move Term Involving x: Move the term involving x to the other side of the equation to isolate the constant on one side.To do this, we subtract 3x from both sides of the equation:y−3x=3x+8−3xThis simplifies to:y−3x=8
Rearrange Terms to Match: Rearrange the terms to match the standard form Ax+By=C. We want the x term first, followed by the y term, equaling the constant: −3x+y=8
Ensure Non-Negative Coefficient: Ensure that the coefficient of x is non-negative.If we multiply the entire equation by −1, we get:3x−y=−8However, since the coefficient of x in the original rearrangement (−3x+y=8) is negative, we do not need to multiply by −1 because the standard form does not require A to be positive, only non-negative. Therefore, we can leave the equation as −3x+y=8.
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