Write The Linear Equation $x=-\frac{5}{6} Y-\frac{5}{6}$ In Standard Form.A. 6 X + 5 Y = − 5 6x + 5y = -5 6 X + 5 Y = − 5 B. 6 X − 5 Y = − 5 6x - 5y = -5 6 X − 5 Y = − 5 C. 6 X + 5 Y = 5 6x + 5y = 5 6 X + 5 Y = 5 D. 6 X − 5 Y = 5 6x - 5y = 5 6 X − 5 Y = 5

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Introduction

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In mathematics, linear equations are a fundamental concept in algebra and geometry. They are used to represent a relationship between two or more variables. A linear equation is typically written in the form of ax + by = c, where a, b, and c are constants, and x and y are variables. However, not all linear equations are written in this standard form. In this article, we will explore how to convert a linear equation to its standard form.

What is Standard Form?

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The standard form of a linear equation is ax + by = c, where a, b, and c are constants, and x and y are variables. The standard form is also known as the general form of a linear equation. It is called the standard form because it is the most common way to write a linear equation.

Converting a Linear Equation to Standard Form

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To convert a linear equation to its standard form, we need to follow these steps:

1. Isolate the variable x: The first step is to isolate the variable x on one side of the equation. This can be done by adding or subtracting the same value to both sides of the equation.
2. Multiply both sides by a constant: Once the variable x is isolated, we need to multiply both sides of the equation by a constant to make the coefficient of x equal to 1.
3. Add or subtract a constant: After multiplying both sides by a constant, we need to add or subtract a constant to make the coefficient of y equal to 1.

Example: Converting the Linear Equation $x=-\frac{5}{6} y-\frac{5}{6}$ to Standard Form

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Let's take the linear equation $x=-\frac{5}{6} y-\frac{5}{6}$ as an example. To convert this equation to its standard form, we need to follow the steps outlined above.

Step 1: Isolate the variable x

The first step is to isolate the variable x on one side of the equation. We can do this by adding $\frac{5}{6}$ to both sides of the equation.

$$x + \frac{5}{6} = -\frac{5}{6} y$$

Step 2: Multiply both sides by a constant

Once the variable x is isolated, we need to multiply both sides of the equation by a constant to make the coefficient of x equal to 1. In this case, we can multiply both sides by 6.

$$6x + 5 = -5y$$

Step 3: Add or subtract a constant

After multiplying both sides by a constant, we need to add or subtract a constant to make the coefficient of y equal to 1. In this case, we can add 5 to both sides of the equation.

$$6x + 5y = -5$$

Conclusion

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In conclusion, converting a linear equation to its standard form is a straightforward process that involves isolating the variable x, multiplying both sides by a constant, and adding or subtracting a constant. By following these steps, we can convert any linear equation to its standard form.

Answer

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The correct answer is:

• A. $6x + 5y = -5$

This is the standard form of the linear equation $x=-\frac{5}{6} y-\frac{5}{6}$.

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Introduction

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In our previous article, we discussed how to convert a linear equation to its standard form. However, we understand that some readers may still have questions about this topic. In this article, we will address some of the most frequently asked questions (FAQs) about converting linear equations to standard form.

Q: What is the standard form of a linear equation?

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A: The standard form of a linear equation is ax + by = c, where a, b, and c are constants, and x and y are variables.

Q: How do I convert a linear equation to its standard form?

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A: To convert a linear equation to its standard form, you need to follow these steps:

1. Isolate the variable x on one side of the equation.
2. Multiply both sides of the equation by a constant to make the coefficient of x equal to 1.
3. Add or subtract a constant to make the coefficient of y equal to 1.

Q: What if the linear equation has a negative coefficient?

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A: If the linear equation has a negative coefficient, you can multiply both sides of the equation by -1 to make the coefficient positive.

Q: Can I convert a linear equation to its standard form if it has a fraction?

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A: Yes, you can convert a linear equation to its standard form even if it has a fraction. To do this, you need to multiply both sides of the equation by the denominator of the fraction.

Q: How do I know if a linear equation is in standard form?

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A: A linear equation is in standard form if it is in the form ax + by = c, where a, b, and c are constants, and x and y are variables.

Q: Can I convert a linear equation to its standard form if it has a variable on both sides?

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A: Yes, you can convert a linear equation to its standard form even if it has a variable on both sides. To do this, you need to isolate the variable on one side of the equation and then follow the steps outlined above.

Q: What if I make a mistake while converting a linear equation to its standard form?

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A: If you make a mistake while converting a linear equation to its standard form, you can try to identify the error and correct it. If you are still having trouble, you can try to rework the problem from the beginning.

Q: Can I use a calculator to convert a linear equation to its standard form?

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A: Yes, you can use a calculator to convert a linear equation to its standard form. However, it's always a good idea to double-check your work to make sure that the equation is in standard form.

Conclusion

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In conclusion, converting a linear equation to its standard form is a straightforward process that involves isolating the variable x, multiplying both sides by a constant, and adding or subtracting a constant. By following these steps and addressing some of the most frequently asked questions about this topic, we hope to have provided you with a better understanding of how to convert linear equations to their standard form.

Additional Resources

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If you are still having trouble converting linear equations to their standard form, you may want to try the following resources:

• Online tutorials and videos
• Math textbooks and workbooks
• Online math communities and forums
• Math tutors and instructors

We hope that this article has been helpful in addressing some of the most frequently asked questions about converting linear equations to their standard form. If you have any further questions or concerns, please don't hesitate to ask.