Rewrite The Equation $4x + 4y = 20$ In Slope-intercept Form.A. $4x + 4y - 20 = 0$ B. $4y = -4x + 20$ C. $y = -x + 5$ D. $x + Y = 5$

Introduction

In mathematics, the slope-intercept form of a linear equation is a way to express the equation in the form $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept. This form is useful for graphing lines and understanding their properties. In this article, we will rewrite the equation $4x + 4y = 20$ in slope-intercept form.

Understanding the Equation

The given equation is $4x + 4y = 20$. To rewrite this equation in slope-intercept form, we need to isolate the variable $y$ on one side of the equation. We can start by subtracting $4x$ from both sides of the equation.

Subtracting $4x$ from Both Sides

Subtracting $4x$ from both sides of the equation gives us:

$$4y = -4x + 20$$

Isolating $y$

Now, we can isolate $y$ by dividing both sides of the equation by $4$.

Dividing Both Sides by $4$

Dividing both sides of the equation by $4$ gives us:

$$y = -x + 5$$

Conclusion

We have successfully rewritten the equation $4x + 4y = 20$ in slope-intercept form. The final answer is $y = -x + 5$. This form is useful for graphing lines and understanding their properties.

Answer Key

The correct answer is C. $y = -x + 5$.

Why is Slope-Intercept Form Important?

Slope-intercept form is an important concept in mathematics because it allows us to easily identify the slope and y-intercept of a line. This information is useful for graphing lines and understanding their properties. In addition, slope-intercept form is often used in real-world applications, such as calculating the cost of goods sold or determining the interest rate on a loan.

Real-World Applications of Slope-Intercept Form

Slope-intercept form has many real-world applications. For example, in business, slope-intercept form can be used to calculate the cost of goods sold. If a company sells a product for $10 and the cost of goods sold is $5, then the profit is $5. This can be represented by the equation $y = 5x + 5$, where $y$ is the profit and $x$ is the number of units sold.

In finance, slope-intercept form can be used to determine the interest rate on a loan. If a person borrows $10,000 at an interest rate of 5%, then the interest paid per year is $500. This can be represented by the equation $y = 0.05x$, where $y$ is the interest paid and $x$ is the principal amount borrowed.

Conclusion

In conclusion, slope-intercept form is an important concept in mathematics that allows us to easily identify the slope and y-intercept of a line. This information is useful for graphing lines and understanding their properties. Slope-intercept form has many real-world applications, such as calculating the cost of goods sold and determining the interest rate on a loan.

Final Answer

Q: What is slope-intercept form?

A: Slope-intercept form is a way to express a linear equation in the form $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept.

Q: Why is slope-intercept form important?

A: Slope-intercept form is important because it allows us to easily identify the slope and y-intercept of a line. This information is useful for graphing lines and understanding their properties.

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 subtracting $x$ from both sides of the equation and then dividing both sides by the coefficient of $y$.

Q: What is the slope of a line in slope-intercept form?

A: The slope of a line in slope-intercept form is the coefficient of $x$, which is represented by $m$.

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

A: The y-intercept of a line in slope-intercept form is the constant term, which is represented by $b$.

Q: How do I graph a line in slope-intercept form?

A: To graph a line in slope-intercept form, you need to find the y-intercept and the slope. The y-intercept is the point where the line intersects the y-axis, and the slope is the rate of change of the line.

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

A: Slope-intercept form has many real-world applications, such as calculating the cost of goods sold, determining the interest rate on a loan, and graphing lines.

Q: Can I use slope-intercept form to solve systems of equations?

A: Yes, you can use slope-intercept form to solve systems of equations. By graphing the lines in slope-intercept form, you can find the point of intersection, which represents the solution to the system of equations.

Q: What are some common mistakes to avoid when working with slope-intercept form?

A: Some common mistakes to avoid when working with slope-intercept form include:

• Not isolating the variable $y$ on one side of the equation
• Not dividing both sides of the equation by the coefficient of $y$
• Not finding the y-intercept and the slope
• Not graphing the line correctly

Conclusion

In conclusion, slope-intercept form is an important concept in mathematics that allows us to easily identify the slope and y-intercept of a line. This information is useful for graphing lines and understanding their properties. By following the steps outlined in this article, you can master the concept of slope-intercept form and apply it to real-world problems.

Final Answer

The final answer is C. $y = -x + 5$.