What Is Y = 2 3 X + 4 Y = \frac{2}{3}x + 4 Y = 3 2 ​ X + 4 Written In Standard Form?Choose 1 Answer:A. 3 Y = 2 X + 12 3y = 2x + 12 3 Y = 2 X + 12 B. − 2 X + 3 Y = 12 -2x + 3y = 12 − 2 X + 3 Y = 12 C. Y − 2 3 X − 4 = 0 Y - \frac{2}{3}x - 4 = 0 Y − 3 2 ​ X − 4 = 0 D. Y = 2 3 ( X + 6 Y = \frac{2}{3}(x + 6 Y = 3 2 ​ ( X + 6 ]

What is $y = \frac{2}{3}x + 4$ written in standard form?

Understanding the Standard Form of a Linear Equation

The standard form of a linear equation is a way of expressing a linear equation in a specific format. It is often used in mathematics and algebra to simplify and solve equations. In the standard form, the equation is written as $Ax + By = C$, where $A$, $B$, and $C$ are constants, and $x$ and $y$ are variables.

Converting the Given Equation to Standard Form

The given equation is $y = \frac{2}{3}x + 4$. To convert this equation to standard form, we need to isolate the variable $y$ on one side of the equation. We can do this by subtracting $\frac{2}{3}x$ from both sides of the equation.

Step 1: Subtract $\frac{2}{3}x$ from both sides

Subtracting $\frac{2}{3}x$ from both sides of the equation gives us:

$$y - \frac{2}{3}x = 4$$

Step 2: Multiply both sides by 3 to eliminate the fraction

To eliminate the fraction, we can multiply both sides of the equation by 3. This gives us:

$$3(y - \frac{2}{3}x) = 3(4)$$

Step 3: Distribute the 3 to the terms inside the parentheses

Distributing the 3 to the terms inside the parentheses gives us:

$$3y - 2x = 12$$

Step 4: Rearrange the equation to the standard form

Rearranging the equation to the standard form gives us:

$$-2x + 3y = 12$$

Conclusion

Therefore, the equation $y = \frac{2}{3}x + 4$ written in standard form is:

$$-2x + 3y = 12$$

This is the correct answer.

Answer

The correct answer is:

B. $-2x + 3y = 12$

Explanation

The standard form of a linear equation is $Ax + By = C$. In this case, we have $-2x + 3y = 12$, which is in the standard form. The other options are not in the standard form, so they are not correct.

Key Takeaways

• The standard form of a linear equation is $Ax + By = C$.
• To convert an equation to standard form, we need to isolate the variable on one side of the equation.
• We can eliminate fractions by multiplying both sides of the equation by the denominator.
• The correct answer is B. $-2x + 3y = 12$.
  Q&A: Standard Form of a Linear Equation

Understanding the Standard Form of a Linear Equation

The standard form of a linear equation is a way of expressing a linear equation in a specific format. It is often used in mathematics and algebra to simplify and solve equations. In the standard form, the equation is written as $Ax + By = C$, where $A$, $B$, and $C$ are constants, and $x$ and $y$ are variables.

Frequently Asked Questions

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

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 an equation to standard form?

A: To convert an equation to standard form, you need to isolate the variable on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What if the equation has a fraction?

A: If the equation has a fraction, you can eliminate it by multiplying both sides of the equation by the denominator.

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

A: An equation is in standard form if it is written as $Ax + By = C$, where $A$, $B$, and $C$ are constants, and $x$ and $y$ are variables.

Q: Can I have multiple answers for a standard form equation?

A: No, a standard form equation should have only one solution. If you have multiple answers, it means that the equation is not in standard form.

Q: What if I have a linear equation with two variables?

A: If you have a linear equation with two variables, you can still convert it to standard form by isolating one of the variables on one side of the equation.

Q: Can I use the standard form of a linear equation to solve systems of equations?

A: Yes, you can use the standard form of a linear equation to solve systems of equations. By converting each equation to standard form, you can then use substitution or elimination methods to solve the system.

Q: What are some common mistakes to avoid when converting an equation to standard form?

A: Some common mistakes to avoid when converting an equation to standard form include:

• Not isolating the variable on one side of the equation
• Not eliminating fractions
• Not checking if the equation is in standard form

Conclusion

The standard form of a linear equation is a powerful tool in mathematics and algebra. By understanding how to convert an equation to standard form, you can simplify and solve equations with ease. Remember to isolate the variable on one side of the equation, eliminate fractions, and check if the equation is in standard form.

Key Takeaways

• The standard form of a linear equation is $Ax + By = C$.
• To convert an equation to standard form, isolate the variable on one side of the equation.
• Eliminate fractions by multiplying both sides of the equation by the denominator.
• Check if the equation is in standard form by verifying that it is written as $Ax + By = C$.

Additional Resources

• For more information on the standard form of a linear equation, check out the following resources:

• Khan Academy: Standard Form of a Linear Equation
• Mathway: Standard Form of a Linear Equation
• Wolfram Alpha: Standard Form of a Linear Equation