Rewrite the following equation in standard form.y=5x+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=5x+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: Identify the given equation and the standard form requirement.The given equation is y=5x+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 for Isolation: Move the term involving x to the other side of the equation to isolate y. To do this, we subtract 5x from both sides of the equation. y−5x=4−5x This results in −5x+y=4, which is almost in standard form, but we typically want the x-term to be positive.
Make Coefficient Positive: Multiply the entire equation by −1 to make the coefficient of x positive.Multiplying by −1, we get:−1(−5x+y)=−1(4)5x−y=−4Now, we have the x-term positive, but the y-term is negative.
Rearrange for Standard Form: Rearrange the terms to match the standard form Ax+By=C. We want the equation to be in the form of Ax+By=C, so we move the y-term to the other side by adding y to both sides. 5x−y+y=−4+y This simplifies to: 5x+0y=−4+y Which is the same as: 5x=y−4 However, we need to have both x and y on the same side, so we add y to both sides to get the final standard form. 5x+y=4
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