Q. Determine the standard form of the following equation:y=8x−7
Identify Equation: Identify the given equation and the standard form requirement.The given equation is y=8x−7, and 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 for Isolation: Move the term involving x to the other side of the equation to isolate y. To do this, we subtract 8x from both sides of the equation. y=8x−7y−8x=−7
Rearrange for Standard Form: Rearrange the terms to match the standard form Ax+By=C. We want the x term to come before the y term, so we write the equation as: −8x+y=−7
Ensure Non-Negative Coefficient: Ensure that the coefficient of x is non-negative.If the coefficient of x is negative, we can multiply the entire equation by −1 to make it positive.−1(−8x+y)=−1(−7)8x−y=7
Check for GCF: Check if the coefficients have a GCF other than 1. The coefficients are 8, −1, and 7. The GCF of these numbers is 1, so we do not need to divide the entire equation by any number.
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