Q. Determine the standard form of the following equation:y=10x+10
Start with given equation: To rewrite the equation in standard form, we need to rearrange the terms so that the x and y terms are on the left side of the equation and the constant is on the right side. We start with the given equation:y=10x+10
Move x term to other side: We want to move the term involving x to the other side of the equation. To do this, we can subtract 10x from both sides of the equation:y−10x=10x+10−10x
Simplify right side: Simplifying the right side of the equation, we get:y−10x=10This is almost in standard form, but the terms on the left side are not in the conventional order.
Rearrange terms in standard form: The standard form of a linear equation is Ax+By=C. We need to rearrange the terms on the left side to reflect this order:−10x+y=10
Make coefficient A positive: However, the coefficient A in standard form should be positive. To achieve this, we can multiply the entire equation by −1: −1(−10x+y)=−1(10)
Make coefficient A positive: However, the coefficient A in standard form should be positive. To achieve this, we can multiply the entire equation by −1: −1(−10x+y)=−1(10) Multiplying through, we get: 10x−y=−10Now the equation is in standard form with A positive.
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