Convert Y = 1/2x + 4 To Standard Form

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Converting the equation Y = 1/2x + 4 to standard form is a fundamental concept in algebra. The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. To convert the given equation to standard form, we'll perform a series of simple steps.

What is Standard Form?

Standard form is a way of writing a linear equation in a specific format. It's used to represent a line on a graph. The standard form of a linear equation is:

Ax + By = C

Where:

• A is the coefficient of x (the number in front of the x)
• B is the coefficient of y (the number in front of the y)
• C is the constant term

Converting Y = 1/2x + 4 to Standard Form

To convert the equation Y = 1/2x + 4 to standard form, we need to rearrange the terms to match the standard form format. Here's the step-by-step process:

Step 1: Multiply Both Sides by 2

To eliminate the fraction, multiply both sides of the equation by 2. This will get rid of the 1/2 coefficient.

2Y = 2(1/2x + 4)

This simplifies to:

2Y = x + 8

Step 2: Rearrange the Terms

Now, let's rearrange the terms to match the standard form format. Subtract x from both sides and add 8 to both sides:

-x + 2Y = 8

Step 3: Write the Equation in Standard Form

The equation is now in standard form:

-x + 2Y = 8

Or, if you prefer to have a positive coefficient for x:

x - 2Y = -8

Benefits of Standard Form

Writing equations in standard form has several benefits. It allows us to:

• Easily identify the coefficients and constant term
• Compare equations and determine if they are equivalent
• Graph lines on a coordinate plane
• Solve systems of linear equations

Conclusion

Converting the equation Y = 1/2x + 4 to standard form is a simple process that involves multiplying both sides by a coefficient and rearranging the terms. The resulting equation, x - 2Y = -8, is in standard form and can be used for graphing, comparing, and solving systems of linear equations.