Rewrite the following equation in standard form.y=4x+6Hint: 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=4x+6Hint: 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=4x−6. 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: Move the term involving x to the other side of the equation to isolate the constant term.To do this, we subtract 4x from both sides of the equation.y−4x=−6However, this is not the standard form because the x term should be on the left side of the equation.
Rearrange Terms: Rearrange the terms to place the x term on the left side and the y term on the right side.We write the x term first, followed by the y term, to get the equation in standard form.−4x+y=−6
Ensure Positive Coefficient: Ensure that the coefficient of x is positive.Since the standard form requires the coefficient of x to be positive, we multiply the entire equation by −1 to get the positive coefficient for x.−1(−4x+y)=−1(−6)4x−y=6
Check Coefficients: Check if the coefficients are integers with a GCF of 1.The coefficients 4, −1, and 6 are all integers, and their GCF is 1.
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