Rewrite the following equation in standard form.y=4x+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=4x+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: Identify the given equation and the standard form requirement.The given equation is y=4x−5. 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=−5However, this is not the standard form yet 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=−5
Ensure Positive Coefficient: Ensure that the coefficient of x is positive.Since the standard form requires the coefficient of x to be non-negative, we multiply the entire equation by −1 to make the coefficient of x positive.−1(−4x+y)=−1(−5)4x−y=5
Check GCF: Check if the coefficients have a GCF other than 1. The coefficients are 4, −1, and 5. The GCF of these numbers is 1, so we do not need to divide the entire equation by any number to reduce the coefficients.
More problems from Write linear equations in standard form