A Line Has A Slope Of 0 And A $y$-intercept Of $\frac{8}{5}$. Write Its Equation In Slope-intercept Form.Write Your Answer Using Integers, Proper Fractions, And Improper Fractions In Simplest Form.

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Introduction

In mathematics, the slope-intercept form of a line is a fundamental concept that helps us understand the relationship between the slope and the $y$-intercept of a line. The slope-intercept form is given by the equation $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. In this article, we will explore the equation of a line with a slope of 0 and a $y$-intercept of $\frac{8}{5}$.

Understanding the Slope-Intercept Form

The slope-intercept form of a line is a powerful tool that allows us to visualize the relationship between the slope and the $y$-intercept of a line. The slope, denoted by $m$, represents the rate of change of the line, while the $y$-intercept, denoted by $b$, represents the point at which the line intersects the $y$-axis. In the equation $y = mx + b$, the slope $m$ is multiplied by the $x$-coordinate of a point on the line, and the result is added to the $y$-intercept $b$.

The Equation of a Line with a Slope of 0

When the slope of a line is 0, it means that the line is horizontal. A horizontal line has the same $y$-coordinate at every point on the line. In other words, the $y$-coordinate does not change as we move along the line. Since the slope is 0, the equation of the line can be written as $y = 0x + b$, where $b$ is the $y$-intercept.

Finding the Equation of the Line

Given that the $y$-intercept of the line is $\frac{8}{5}$, we can substitute this value into the equation $y = 0x + b$ to find the equation of the line. The equation becomes $y = 0x + \frac{8}{5}$.

Simplifying the Equation

To simplify the equation, we can rewrite it as $y = \frac{8}{5}$. This is because the term $0x$ is equal to 0, and when we add 0 to a number, the result is the same number.

Conclusion

In conclusion, the equation of a line with a slope of 0 and a $y$-intercept of $\frac{8}{5}$ is $y = \frac{8}{5}$. This equation represents a horizontal line that intersects the $y$-axis at the point $\left(0, \frac{8}{5}\right)$. The slope-intercept form of a line is a powerful tool that helps us understand the relationship between the slope and the $y$-intercept of a line.

Examples and Applications

Here are a few examples and applications of the equation $y = \frac{8}{5}$:

• Graphing the Line: To graph the line, we can plot the point $\left(0, \frac{8}{5}\right)$ on the $y$-axis and draw a horizontal line through this point.
• Finding the $y$-Coordinate: To find the $y$-coordinate of a point on the line, we can substitute the $x$-coordinate into the equation $y = \frac{8}{5}$.
• Solving for $x$: To solve for $x$, we can rearrange the equation $y = \frac{8}{5}$ to isolate $x$. However, since the equation is in the form $y = mx + b$, where $m = 0$, we cannot solve for $x$.

Exercises and Problems

Here are a few exercises and problems to help you practice working with the equation $y = \frac{8}{5}$:

• Exercise 1: Graph the line $y = \frac{8}{5}$ and find the $y$-coordinate of the point $\left(2, y\right)$.
• Exercise 2: Find the equation of a line with a slope of 0 and a $y$-intercept of $\frac{3}{4}$.
• Problem: A horizontal line intersects the $y$-axis at the point $\left(0, \frac{5}{3}\right)$. Find the equation of the line.

Solutions to Exercises and Problems

Here are the solutions to the exercises and problems:

• Exercise 1: To graph the line, we can plot the point $\left(0, \frac{8}{5}\right)$ on the $y$-axis and draw a horizontal line through this point. To find the $y$-coordinate of the point $\left(2, y\right)$, we can substitute $x = 2$ into the equation $y = \frac{8}{5}$, which gives us $y = \frac{8}{5}$.
• Exercise 2: The equation of a line with a slope of 0 and a $y$-intercept of $\frac{3}{4}$ is $y = \frac{3}{4}$.
• Problem: The equation of the line is $y = \frac{5}{3}$.

Conclusion

In conclusion, the equation of a line with a slope of 0 and a $y$-intercept of $\frac{8}{5}$ is $y = \frac{8}{5}$. This equation represents a horizontal line that intersects the $y$-axis at the point $\left(0, \frac{8}{5}\right)$. The slope-intercept form of a line is a powerful tool that helps us understand the relationship between the slope and the $y$-intercept of a line.

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Introduction

In our previous article, we explored the equation of a line with a slope of 0 and a $y$-intercept of $\frac{8}{5}$. In this article, we will answer some frequently asked questions about this topic.

Q&A

Q: What is the equation of a line with a slope of 0 and a $y$-intercept of $\frac{8}{5}$?

A: The equation of a line with a slope of 0 and a $y$-intercept of $\frac{8}{5}$ is $y = \frac{8}{5}$.

Q: What does the slope of 0 mean in the context of a line?

A: The slope of 0 means that the line is horizontal. A horizontal line has the same $y$-coordinate at every point on the line.

Q: What is the $y$-intercept of a line?

A: The $y$-intercept of a line is the point at which the line intersects the $y$-axis. In the equation $y = mx + b$, the $y$-intercept is represented by the term $b$.

Q: How do I graph a line with a slope of 0 and a $y$-intercept of $\frac{8}{5}$?

A: To graph a line with a slope of 0 and a $y$-intercept of $\frac{8}{5}$, you can plot the point $\left(0, \frac{8}{5}\right)$ on the $y$-axis and draw a horizontal line through this point.

Q: Can I solve for $x$ in the equation $y = \frac{8}{5}$?

A: No, you cannot solve for $x$ in the equation $y = \frac{8}{5}$ because the equation is in the form $y = mx + b$, where $m = 0$. Since the slope is 0, the equation does not have a solution for $x$.

Q: What is the relationship between the slope and the $y$-intercept of a line?

A: The slope and the $y$-intercept of a line are related in the equation $y = mx + b$. The slope $m$ represents the rate of change of the line, while the $y$-intercept $b$ represents the point at which the line intersects the $y$-axis.

Q: Can I find the equation of a line with a slope of 0 and a $y$-intercept of $\frac{3}{4}$?

A: Yes, you can find the equation of a line with a slope of 0 and a $y$-intercept of $\frac{3}{4}$ by substituting the values into the equation $y = mx + b$. The equation becomes $y = 0x + \frac{3}{4}$, which simplifies to $y = \frac{3}{4}$.

Conclusion

In conclusion, the equation of a line with a slope of 0 and a $y$-intercept of $\frac{8}{5}$ is $y = \frac{8}{5}$. This equation represents a horizontal line that intersects the $y$-axis at the point $\left(0, \frac{8}{5}\right)$. The slope-intercept form of a line is a powerful tool that helps us understand the relationship between the slope and the $y$-intercept of a line.

Additional Resources

• Graphing Lines: To learn more about graphing lines, check out our article on graphing lines.
• Slope-Intercept Form: To learn more about the slope-intercept form of a line, check out our article on the slope-intercept form.
• Mathematics: To learn more about mathematics, check out our article on mathematics.

Exercises and Problems

Here are a few exercises and problems to help you practice working with the equation $y = \frac{8}{5}$:

• Exercise 1: Graph the line $y = \frac{8}{5}$ and find the $y$-coordinate of the point $\left(2, y\right)$.
• Exercise 2: Find the equation of a line with a slope of 0 and a $y$-intercept of $\frac{3}{4}$.
• Problem: A horizontal line intersects the $y$-axis at the point $\left(0, \frac{5}{3}\right)$. Find the equation of the line.

Solutions to Exercises and Problems

Here are the solutions to the exercises and problems:

• Exercise 1: To graph the line, you can plot the point $\left(0, \frac{8}{5}\right)$ on the $y$-axis and draw a horizontal line through this point. To find the $y$-coordinate of the point $\left(2, y\right)$, you can substitute $x = 2$ into the equation $y = \frac{8}{5}$, which gives us $y = \frac{8}{5}$.
• Exercise 2: The equation of a line with a slope of 0 and a $y$-intercept of $\frac{3}{4}$ is $y = \frac{3}{4}$.
• Problem: The equation of the line is $y = \frac{5}{3}$.