Rewrite the following equation in standard form.y=2x+10Hint: 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=2x+10Hint: 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=2x+10. 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 on one side.To do this, we subtract 2x from both sides of the equation.y−2x=2x+10−2xThis simplifies to:y−2x=10
Rearrange for Standard Form: Rearrange the terms to match the standard form Ax+By=C. We want the x term first, followed by the y term, equaling the constant. −2x+y=10
Ensure Non-Negative Coefficient: Ensure that the coefficient of x is non-negative.If we multiply the entire equation by −1, we will get the coefficient of x to be positive, which is a common convention for standard form.(−1)(−2x)+(−1)y=(−1)10This simplifies to:2x−y=−10
Check GCF: Check if the coefficients have a GCF other than 1. The coefficients are 2, −1, and −10. The GCF of these numbers is 1.
More problems from Write linear equations in standard form