Is The Point { (0, -3)$}$ A Solution To The Inequality { Y \ \textgreater \ \frac{4}{5}x - 3$}$?

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Introduction

In mathematics, inequalities are used to describe relationships between variables. A solution to an inequality is a value or set of values that satisfy the inequality. In this article, we will explore whether the point {(0, -3)$}$ is a solution to the inequality {y \ \textgreater \ \frac{4}{5}x - 3$}$. To determine this, we need to substitute the coordinates of the point into the inequality and check if it holds true.

Understanding the Inequality

The given inequality is {y \ \textgreater \ \frac{4}{5}x - 3$}$. This means that the value of {y$}$ must be greater than the value of {\frac{4}{5}x - 3$}$ for the inequality to hold true. We can rewrite the inequality as {y - \frac{4}{5}x + 3 \ \textgreater \ 0$}$ to make it easier to work with.

Substituting the Point into the Inequality

To check if the point {(0, -3)$}$ is a solution to the inequality, we need to substitute the coordinates into the inequality. We will substitute {x = 0$}$ and {y = -3$}$ into the inequality.

Calculating the Value of the Inequality

Substituting {x = 0$}$ and {y = -3$}$ into the inequality, we get:

{-3 - \frac{4}{5}(0) + 3 \ \textgreater \ 0$}$

Simplifying the expression, we get:

{-3 + 3 \ \textgreater \ 0$}$

${0 \ \textgreater \ 0\$}

This is a true statement, which means that the point {(0, -3)$}$ satisfies the inequality.

Conclusion

In conclusion, the point {(0, -3)$}$ is a solution to the inequality {y \ \textgreater \ \frac{4}{5}x - 3$}$. This is because when we substitute the coordinates of the point into the inequality, we get a true statement.

Understanding the Graph of the Inequality

The graph of the inequality {y \ \textgreater \ \frac{4}{5}x - 3$}$ is a line with a slope of {\frac{4}{5}$}$ and a y-intercept of {-3$}$. The line is drawn with a solid line, and the region above the line is shaded to indicate that the inequality is satisfied.

Visualizing the Solution

To visualize the solution, we can plot the point {(0, -3)$}$ on the graph of the inequality. Since the point lies above the line, it satisfies the inequality.

Implications of the Solution

The solution to the inequality has implications in various fields, such as economics and engineering. For example, in economics, the inequality can be used to model the relationship between the price of a good and the quantity demanded. In engineering, the inequality can be used to design systems that meet certain performance criteria.

Real-World Applications

The inequality {y \ \textgreater \ \frac{4}{5}x - 3$}$ has various real-world applications. For example, in finance, the inequality can be used to model the relationship between the interest rate and the amount borrowed. In transportation, the inequality can be used to design routes that minimize travel time.

Conclusion

In conclusion, the point {(0, -3)$}$ is a solution to the inequality {y \ \textgreater \ \frac{4}{5}x - 3$}$. This is because when we substitute the coordinates of the point into the inequality, we get a true statement. The solution to the inequality has implications in various fields and has various real-world applications.

Final Thoughts

The inequality {y \ \textgreater \ \frac{4}{5}x - 3$}$ is a simple yet powerful tool for modeling relationships between variables. By understanding the solution to the inequality, we can gain insights into various fields and make informed decisions.

References

Note: The references provided are for educational purposes only and are not intended to be a comprehensive list of sources.

Introduction

In our previous article, we explored whether the point {(0, -3)$}$ is a solution to the inequality {y \ \textgreater \ \frac{4}{5}x - 3$}$. In this article, we will answer some frequently asked questions related to the inequality and its solution.

Q: What is the inequality {y \ \textgreater \ \frac{4}{5}x - 3$}$?

A: The inequality {y \ \textgreater \ \frac{4}{5}x - 3$}$ is a linear inequality that describes a relationship between the variables {x$}$ and {y$}$. The inequality states that the value of {y$}$ must be greater than the value of {\frac{4}{5}x - 3$}$.

Q: What is the solution to the inequality?

A: The solution to the inequality is the set of all points that satisfy the inequality. In this case, the solution is the set of all points that lie above the line {y = \frac{4}{5}x - 3$}$.

Q: Is the point {(0, -3)$}$ a solution to the inequality?

A: Yes, the point {(0, -3)$}$ is a solution to the inequality. When we substitute the coordinates of the point into the inequality, we get a true statement.

Q: How do I graph the inequality?

A: To graph the inequality, we can draw the line {y = \frac{4}{5}x - 3$}$ and shade the region above the line. This will give us a visual representation of the solution to the inequality.

Q: What are some real-world applications of the inequality?

A: The inequality {y \ \textgreater \ \frac{4}{5}x - 3$}$ has various real-world applications. For example, in finance, the inequality can be used to model the relationship between the interest rate and the amount borrowed. In transportation, the inequality can be used to design routes that minimize travel time.

Q: How do I solve a system of linear inequalities?

A: To solve a system of linear inequalities, we can use the following steps:

  1. Graph each inequality on a coordinate plane.
  2. Find the intersection of the two graphs.
  3. Determine the solution to the system by identifying the region that satisfies both inequalities.

Q: What is the difference between a linear inequality and a quadratic inequality?

A: A linear inequality is an inequality that can be written in the form {ax + by \ \textgreater \ c$}$, where {a$}$, {b$}$, and {c$}$ are constants. A quadratic inequality is an inequality that can be written in the form {ax^2 + bx + c \ \textgreater \ 0$}$, where {a$}$, {b$}$, and {c$}$ are constants.

Q: How do I use a graphing calculator to solve a linear inequality?

A: To use a graphing calculator to solve a linear inequality, follow these steps:

  1. Enter the inequality into the calculator.
  2. Graph the inequality on the calculator.
  3. Identify the solution to the inequality by examining the graph.

Q: What are some common mistakes to avoid when solving linear inequalities?

A: Some common mistakes to avoid when solving linear inequalities include:

  • Not reading the inequality correctly.
  • Not graphing the inequality correctly.
  • Not identifying the solution to the inequality correctly.

Conclusion

In conclusion, the inequality {y \ \textgreater \ \frac{4}{5}x - 3$}$ is a simple yet powerful tool for modeling relationships between variables. By understanding the solution to the inequality, we can gain insights into various fields and make informed decisions.

Final Thoughts

The inequality {y \ \textgreater \ \frac{4}{5}x - 3$}$ is a fundamental concept in mathematics that has various real-world applications. By mastering the concept of linear inequalities, we can solve a wide range of problems in various fields.

References

Note: The references provided are for educational purposes only and are not intended to be a comprehensive list of sources.