Rewrite The Equation $2x - 4y = 8$ In Slope-intercept Form.A. $y = 2x - 2$B. $y = \frac{1}{2}x + 2$C. $ Y = − 1 2 X − 2 Y = -\frac{1}{2}x - 2 Y = − 2 1 ​ X − 2 [/tex]D. $y = \frac{1}{2}x - 2$Please Select The Best Answer From

Introduction

In mathematics, the slope-intercept form of a linear equation is a way to express the equation in terms of its slope and y-intercept. This form is particularly useful for graphing and analyzing linear equations. In this article, we will focus on rewriting the equation $2x - 4y = 8$ in slope-intercept form.

Understanding Slope-Intercept Form

The slope-intercept form of a linear equation is given by the equation $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept. The slope-intercept form is a convenient way to express the equation because it allows us to easily identify the slope and y-intercept of the line.

Rewriting the Equation

To rewrite the equation $2x - 4y = 8$ in slope-intercept form, we need to isolate the variable $y$ on one side of the equation. We can do this by adding $4y$ to both sides of the equation and then dividing both sides by $-4$.

$$2x - 4y = 8$$

Adding $4y$ to both sides:

$$2x = 8 + 4y$$

Dividing both sides by $-4$:

$$y = -\frac{1}{2}x + 2$$

Comparing the Options

Now that we have rewritten the equation in slope-intercept form, we can compare our result to the options provided.

• Option A: $y = 2x - 2$
• Option B: $y = \frac{1}{2}x + 2$
• Option C: $y = -\frac{1}{2}x - 2$
• Option D: $y = \frac{1}{2}x - 2$

Our rewritten equation, $y = -\frac{1}{2}x + 2$, matches option C.

Conclusion

In conclusion, we have successfully rewritten the equation $2x - 4y = 8$ in slope-intercept form. By isolating the variable $y$ on one side of the equation and then dividing both sides by $-4$, we were able to express the equation in the form $y = mx + b$. Our rewritten equation matches option C, which is the correct answer.

Final Answer

The final answer is:

• C. $y = -\frac{1}{2}x - 2$

Additional Tips and Tricks

• When rewriting an equation in slope-intercept form, make sure to isolate the variable $y$ on one side of the equation.
• Use the correct signs when dividing both sides of the equation by a negative number.
• Compare your rewritten equation to the options provided to ensure that you have the correct answer.

Common Mistakes to Avoid

• Failing to isolate the variable $y$ on one side of the equation.
• Using the wrong signs when dividing both sides of the equation by a negative number.
• Not comparing the rewritten equation to the options provided.

Real-World Applications

The slope-intercept form of a linear equation has many real-world applications, including:

• Graphing linear equations
• Analyzing linear equations
• Finding the equation of a line given its slope and y-intercept

Conclusion

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Introduction

In our previous article, we discussed how to rewrite the equation $2x - 4y = 8$ in slope-intercept form. In this article, we will answer some frequently asked questions about rewriting equations in slope-intercept form.

Q: What is the slope-intercept form of a linear equation?

A: The slope-intercept form of a linear equation is given by the equation $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept.

Q: How do I rewrite an equation in slope-intercept form?

A: To rewrite an equation in slope-intercept form, you need to isolate the variable $y$ on one side of the equation. You can do this by adding or subtracting the same value to both sides of the equation, and then dividing both sides by the coefficient of $y$.

Q: What is the y-intercept in the slope-intercept form of a linear equation?

A: The y-intercept in the slope-intercept form of a linear equation is the value of $b$ in the equation $y = mx + b$. It represents the point where the line intersects the y-axis.

Q: How do I find the slope of a line given its slope-intercept form?

A: To find the slope of a line given its slope-intercept form, you need to look at the coefficient of $x$ in the equation. The coefficient of $x$ is the slope of the line.

Q: Can I rewrite an equation in slope-intercept form if it is not in the standard form?

A: Yes, you can rewrite an equation in slope-intercept form even if it is not in the standard form. However, you may need to perform additional steps to isolate the variable $y$ on one side of the equation.

Q: What are some common mistakes to avoid when rewriting equations in slope-intercept form?

A: Some common mistakes to avoid when rewriting equations in slope-intercept form include:

• Failing to isolate the variable $y$ on one side of the equation
• Using the wrong signs when dividing both sides of the equation by a negative number
• Not comparing the rewritten equation to the options provided

Q: How do I check my answer when rewriting an equation in slope-intercept form?

A: To check your answer when rewriting an equation in slope-intercept form, you can substitute the values of $x$ and $y$ into the original equation and verify that the equation is true.

Q: What are some real-world applications of rewriting equations in slope-intercept form?

A: Some real-world applications of rewriting equations in slope-intercept form include:

• Graphing linear equations
• Analyzing linear equations
• Finding the equation of a line given its slope and y-intercept

Conclusion

In conclusion, rewriting equations in slope-intercept form is an important skill in mathematics. By following the steps outlined in this article, you can successfully rewrite any linear equation in slope-intercept form. Remember to isolate the variable $y$ on one side of the equation, use the correct signs when dividing both sides of the equation by a negative number, and compare the rewritten equation to the options provided.

Additional Resources

• For more information on rewriting equations in slope-intercept form, check out the following resources:

• Khan Academy: Rewriting Equations in Slope-Intercept Form
• Mathway: Rewriting Equations in Slope-Intercept Form
• Wolfram Alpha: Rewriting Equations in Slope-Intercept Form

Final Tips and Tricks

• Practice rewriting equations in slope-intercept form regularly to improve your skills.
• Use online resources, such as Khan Academy and Mathway, to help you with rewriting equations in slope-intercept form.
• Check your answer by substituting the values of $x$ and $y$ into the original equation and verifying that the equation is true.