Rewrite the following equation in standard form.y=6x+4Hint: 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=6x+4Hint: 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 & Standard Form: Identify the given equation and the standard form requirement.The given equation is y=6x−4, 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 Involving x: Move the term involving x to the other side of the equation to isolate the constant term.To do this, we subtract 6x from both sides of the equation.y−6x=−4
Rearrange Terms to Match: 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: −6x+y=−4
Ensure Non-Negative Coefficient: Ensure that the coefficient of x is non-negative.Since the standard form requires A to be non-negative, we multiply the entire equation by −1 to make the coefficient of x positive.6x−y=4
Check Coefficients for GCF: Check that the coefficients are integers with a GCF of 1. The coefficients are 6, −1, and 4. The GCF of these numbers is 1, so they meet the requirement.
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