Denise Built A Storage Shed. To Cut The Wood, She Rented A Large Electric Saw. The Equation { Y = 15x + 12$}$ Represents The Cost, { Y$}$, To Rent The Saw For { X$}$ Days.Explain What The Slope And

Mar 12, 2025 by ADMIN 198 views

**Understanding the Cost of Renting an Electric Saw**

Introduction

In this article, we will explore the concept of slope and its application in a real-world scenario. Denise, a homeowner, rented an electric saw to cut wood for her storage shed. The cost of renting the saw is represented by the equation ${$ y = 15x + 12$}$, where ${$ y$}$ is the cost in dollars and ${$ x$}$ is the number of days the saw is rented. We will analyze the equation and explain the significance of the slope in this context.

The Equation: A Representation of Cost

The equation ${$ y = 15x + 12$}$ represents the cost of renting the electric saw for ${$ x$}$ days. The equation is in the form of a linear equation, where ${$ y$}$ is the dependent variable (the cost) and ${$ x$}$ is the independent variable (the number of days). The equation can be broken down into two parts: the slope-intercept form and the constant term.

Slope-Intercept Form

The slope-intercept form of a linear equation is ${$ y = mx + b$}$, where ${$ m$}$ is the slope and ${$ b$}$ is the y-intercept. In the equation ${$ y = 15x + 12$}$, the slope is ${ $15\$}$ and the y-intercept is ${ $12\$}$ . The slope represents the rate of change of the cost with respect to the number of days.

The Slope: A Measure of Rate of Change

The slope of the equation ${$ y = 15x + 12$}$ is ${ $15\$}$ . This means that for every additional day the saw is rented, the cost increases by ${ $15\$}$ dollars. The slope is a measure of the rate of change of the cost with respect to the number of days. In this case, the slope is positive, indicating that the cost increases as the number of days increases.

Interpretation of the Slope

The slope of ${ $15\$}$ can be interpreted in several ways:

Cost per day: The slope represents the cost per day of renting the saw. In this case, the cost per day is ${ $15\$}$ dollars.
Rate of change: The slope represents the rate of change of the cost with respect to the number of days. In this case, the cost increases by ${ $15\$}$ dollars for every additional day the saw is rented.
Economic interpretation: The slope can be seen as the marginal cost of renting the saw. In this case, the marginal cost is ${ $15\$}$ dollars per day.

The Y-Intercept: A Representation of Initial Cost

The y-intercept of the equation ${$ y = 15x + 12$}$ is ${ $12\$}$ . The y-intercept represents the initial cost of renting the saw, which is ${ $12\$}$ dollars. This means that even if Denise rents the saw for zero days, she will still have to pay ${ $12\$}$ dollars as an initial fee.

Conclusion

In conclusion, the slope of the equation ${$ y = 15x + 12$}$ represents the rate of change of the cost with respect to the number of days. The slope is ${ $15\$}$ , indicating that the cost increases by ${ $15\$}$ dollars for every additional day the saw is rented. The y-intercept represents the initial cost of renting the saw, which is ${ $12\$}$ dollars. Understanding the slope and y-intercept of the equation can help Denise make informed decisions about renting the electric saw for her storage shed project.

Real-World Applications

The concept of slope and its application in the equation ${$ y = 15x + 12$}$ has several real-world implications:

Economic analysis: The slope can be used to analyze the economic implications of renting the saw. For example, if Denise rents the saw for 10 days, the total cost will be ${ $15(10) + 12 = 162\$}$ dollars.
Decision-making: The slope can be used to make informed decisions about renting the saw. For example, if Denise wants to rent the saw for 5 days, she can calculate the total cost using the equation ${$ y = 15x + 12$}$.
Comparison: The slope can be used to compare the cost of renting the saw with other options. For example, if Denise can rent a different saw for ${ $10\$}$ dollars per day, she can calculate the total cost using the equation ${$ y = 10x + 0$}$.

Final Thoughts

Introduction

In our previous article, we explored the concept of slope and its application in a real-world scenario. Denise, a homeowner, rented an electric saw to cut wood for her storage shed. The cost of renting the saw is represented by the equation ${$ y = 15x + 12$}$, where ${$ y$}$ is the cost in dollars and ${$ x$}$ is the number of days the saw is rented. In this article, we will answer some frequently asked questions about the cost of renting an electric saw.

Q: What is the cost of renting the saw for 5 days?

A: To calculate the cost of renting the saw for 5 days, we can use the equation ${$ y = 15x + 12$}$. Plugging in ${$ x = 5$}$, we get:

${$ y = 15(5) + 12 = 75 + 12 = 87$}$

So, the cost of renting the saw for 5 days is ${ $87\$}$ dollars.

Q: What is the cost per day of renting the saw?

A: The cost per day of renting the saw is represented by the slope of the equation, which is ${ $15\$}$ dollars per day.

Q: What is the initial cost of renting the saw?

A: The initial cost of renting the saw is represented by the y-intercept of the equation, which is ${ $12\$}$ dollars.

Q: How can I use the equation to make informed decisions about renting the saw?

A: You can use the equation to calculate the total cost of renting the saw for a specific number of days. For example, if you want to rent the saw for 10 days, you can plug in ${$ x = 10$}$ into the equation to get the total cost.

Q: Can I compare the cost of renting the saw with other options?

A: Yes, you can compare the cost of renting the saw with other options using the equation. For example, if you can rent a different saw for ${ $10\$}$ dollars per day, you can calculate the total cost using the equation ${$ y = 10x + 0$}$.

Q: What if I want to rent the saw for a fraction of a day?

A: If you want to rent the saw for a fraction of a day, you can use the equation to calculate the cost. For example, if you want to rent the saw for ${ $0.5\$}$ days, you can plug in ${$ x = 0.5$}$ into the equation to get the total cost.

Q: Can I use the equation to calculate the cost of renting multiple saws?

A: Yes, you can use the equation to calculate the cost of renting multiple saws. For example, if you want to rent two saws for 5 days each, you can plug in ${$ x = 5$}$ into the equation twice to get the total cost.

Conclusion

In conclusion, the equation ${$ y = 15x + 12$}$ represents the cost of renting an electric saw for ${$ x$}$ days. The slope of the equation represents the cost per day, which is ${ $15\$}$ dollars. The y-intercept represents the initial cost, which is ${ $12\$}$ dollars. Understanding the equation can help you make informed decisions about renting the saw and compare the cost with other options.

Real-World Applications

The equation ${$ y = 15x + 12$}$ has several real-world applications:

Economic analysis: The equation can be used to analyze the economic implications of renting the saw.
Decision-making: The equation can be used to make informed decisions about renting the saw.
Comparison: The equation can be used to compare the cost of renting the saw with other options.