A Car Is Traveling On A Highway. The Distance (in Miles) From Its Destination And The Time (in Hours) Is Given By The Equation $d = 420 - 65t$. What Is The $d$-intercept Of The Line? (Remember The Slope-intercept Form Is $y = Mx +

Introduction

In mathematics, the slope-intercept form of a line is a fundamental concept that helps us understand the relationship between the variables of a linear equation. The slope-intercept form is given by the equation $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept. In this article, we will explore the concept of the d-intercept of a line, which is a specific type of intercept that occurs when the variable $d$ is the subject of the equation.

The Equation of the Line

The equation of the line is given by $d = 420 - 65t$. In this equation, $d$ represents the distance from the destination in miles, and $t$ represents the time in hours. To find the d-intercept of the line, we need to understand the concept of the d-intercept and how it relates to the slope-intercept form of the line.

What is the d-Intercept?

The d-intercept of a line is the point at which the line intersects the d-axis. In other words, it is the value of $d$ when $t = 0$. To find the d-intercept, we need to substitute $t = 0$ into the equation of the line.

Finding the d-Intercept

To find the d-intercept, we substitute $t = 0$ into the equation of the line:

$d = 420 - 65t$

$d = 420 - 65(0)$

$d = 420 - 0$

$d = 420$

Therefore, the d-intercept of the line is 420 miles.

Conclusion

In conclusion, the d-intercept of a line is the point at which the line intersects the d-axis. To find the d-intercept, we need to substitute $t = 0$ into the equation of the line. In this article, we have explored the concept of the d-intercept and how it relates to the slope-intercept form of the line. We have also found the d-intercept of the line given by the equation $d = 420 - 65t$.

Understanding the Slope-Intercept Form

The slope-intercept form of a line is a fundamental concept in mathematics that helps us understand the relationship between the variables of a linear equation. The slope-intercept form is given by the equation $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept. In this article, we have explored the concept of the d-intercept of a line and how it relates to the slope-intercept form of the line.

The Relationship Between the d-Intercept and the Slope-Intercept Form

The d-intercept of a line is related to the slope-intercept form of the line. In the slope-intercept form, the y-intercept is the point at which the line intersects the y-axis. Similarly, the d-intercept of a line is the point at which the line intersects the d-axis. To find the d-intercept, we need to substitute $t = 0$ into the equation of the line.

The Equation of the Line in Slope-Intercept Form

To find the equation of the line in slope-intercept form, we need to isolate $d$ on one side of the equation. We can do this by adding $65t$ to both sides of the equation:

$d = 420 - 65t$

$d + 65t = 420$

$d + 65t = 420$

$d = -65t + 420$

Therefore, the equation of the line in slope-intercept form is $d = -65t + 420$.

The Slope of the Line

The slope of the line is the coefficient of $t$ in the equation of the line. In this case, the slope of the line is $-65$. The slope of the line represents the rate of change of the distance with respect to time.

The y-Intercept of the Line

The y-intercept of the line is the point at which the line intersects the y-axis. In this case, the y-intercept of the line is 420 miles.

The d-Intercept of the Line

The d-intercept of the line is the point at which the line intersects the d-axis. In this case, the d-intercept of the line is 420 miles.

Conclusion

In conclusion, the d-intercept of a line is the point at which the line intersects the d-axis. To find the d-intercept, we need to substitute $t = 0$ into the equation of the line. In this article, we have explored the concept of the d-intercept and how it relates to the slope-intercept form of the line. We have also found the d-intercept of the line given by the equation $d = 420 - 65t$.

The Importance of the d-Intercept

The d-intercept of a line is an important concept in mathematics that has many practical applications. For example, in physics, the d-intercept of a line can represent the distance traveled by an object over time. In economics, the d-intercept of a line can represent the cost of a product over time.

The d-Intercept in Real-World Applications

The d-intercept of a line has many real-world applications. For example, in physics, the d-intercept of a line can represent the distance traveled by an object over time. In economics, the d-intercept of a line can represent the cost of a product over time.

The d-Intercept in Physics

In physics, the d-intercept of a line can represent the distance traveled by an object over time. For example, if we have a car traveling at a constant speed of 60 miles per hour, the d-intercept of the line can represent the distance traveled by the car over time.

The d-Intercept in Economics

In economics, the d-intercept of a line can represent the cost of a product over time. For example, if we have a company that produces a product at a constant cost of $10 per unit, the d-intercept of the line can represent the cost of the product over time.

Conclusion

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Introduction

In our previous article, we explored the concept of the d-intercept of a line and how it relates to the slope-intercept form of the line. We also found the d-intercept of the line given by the equation $d = 420 - 65t$. In this article, we will answer some frequently asked questions on the d-intercept of a line.

Q: What is the d-intercept of a line?

A: The d-intercept of a line is the point at which the line intersects the d-axis. In other words, it is the value of $d$ when $t = 0$.

Q: How do I find the d-intercept of a line?

A: To find the d-intercept of a line, you need to substitute $t = 0$ into the equation of the line.

Q: What is the relationship between the d-intercept and the slope-intercept form of a line?

A: The d-intercept of a line is related to the slope-intercept form of the line. In the slope-intercept form, the y-intercept is the point at which the line intersects the y-axis. Similarly, the d-intercept of a line is the point at which the line intersects the d-axis.

Q: Can you give an example of how to find the d-intercept of a line?

A: Let's say we have a line given by the equation $d = 420 - 65t$. To find the d-intercept of this line, we need to substitute $t = 0$ into the equation:

$d = 420 - 65t$

$d = 420 - 65(0)$

$d = 420 - 0$

$d = 420$

Therefore, the d-intercept of this line is 420 miles.

Q: What is the significance of the d-intercept of a line?

A: The d-intercept of a line is an important concept in mathematics that has many practical applications. For example, in physics, the d-intercept of a line can represent the distance traveled by an object over time. In economics, the d-intercept of a line can represent the cost of a product over time.

Q: Can you give an example of how the d-intercept of a line is used in real-world applications?

A: Let's say we have a company that produces a product at a constant cost of $10 per unit. The d-intercept of the line can represent the cost of the product over time. For example, if we have a product that costs $10 per unit and we produce 100 units in one hour, the d-intercept of the line can represent the total cost of the product over time.

Q: How do I convert the equation of a line from slope-intercept form to d-intercept form?

A: To convert the equation of a line from slope-intercept form to d-intercept form, you need to isolate $d$ on one side of the equation. You can do this by adding $65t$ to both sides of the equation:

$d = 420 - 65t$

$d + 65t = 420$

$d + 65t = 420$

$d = -65t + 420$

Therefore, the equation of the line in d-intercept form is $d = -65t + 420$.

Q: Can you give an example of how to convert the equation of a line from slope-intercept form to d-intercept form?

A: Let's say we have a line given by the equation $y = 2x + 3$. To convert this equation to d-intercept form, we need to isolate $d$ on one side of the equation:

$y = 2x + 3$

$y - 2x = 3$

$y - 2x = 3$

$d = -2x + 3$

Therefore, the equation of the line in d-intercept form is $d = -2x + 3$.

Conclusion

In conclusion, the d-intercept of a line is an important concept in mathematics that has many practical applications. The d-intercept of a line can represent the distance traveled by an object over time, the cost of a product over time, and many other real-world applications. In this article, we have answered some frequently asked questions on the d-intercept of a line and provided examples of how to find the d-intercept of a line and convert the equation of a line from slope-intercept form to d-intercept form.