Rewrite the following equation in standard form.y=7x+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=7x+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 Requirement: Identify the given equation and the standard form requirement.The given equation is y=7x+5, 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 to Left: Move the term involving x to the left side of the equation.To do this, we subtract 7x from both sides of the equation to get −7x+y=5.
Check Coefficient GCF: Check if the coefficients have a GCF other than 1. The coefficients of the terms −7x and y are −7 and 1, respectively. Their GCF is 1, so we do not need to divide the entire equation by any number to reduce the coefficients.
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 get 7x−y=−5.
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