The Table Represents The Equation \[$ Y = 2 - 4x \$\].$\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline -2 & 10 \\ \hline -1 & \\ \hline 0 & 2 \\ \hline 1 & -2 \\ \hline 2 & -6 \\ \hline \end{tabular} \\]Use The Drop-down Menus To

Introduction

In mathematics, equations are used to represent relationships between variables. A table can be used to represent an equation, where the values of the variables are given in a tabular form. In this article, we will analyze the table that represents the equation $y = 2 - 4x$ and explore its properties and characteristics.

Understanding the Equation

The given equation is a linear equation in the form of $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. In this case, the equation is $y = 2 - 4x$, where the slope is $-4$ and the y-intercept is $2$. This means that for every unit increase in $x$, the value of $y$ decreases by $4$ units.

Analyzing the Table

The table represents the equation $y = 2 - 4x$ with different values of $x$ and the corresponding values of $y$. Let's analyze the table and see how it represents the equation.

x	y
-2	10
-1
0	2
1	-2
2	-6

Finding the Missing Value

The table has a missing value for $x = -1$. To find the missing value, we can substitute $x = -1$ into the equation $y = 2 - 4x$. This gives us:

$y = 2 - 4(-1)$ $y = 2 + 4$ $y = 6$

Therefore, the missing value for $x = -1$ is $y = 6$.

Verifying the Equation

Now that we have the missing value, let's verify that the table represents the equation $y = 2 - 4x$. We can do this by substituting the values of $x$ and $y$ from the table into the equation and checking if it holds true.

For $x = -2$, we have:

$y = 2 - 4(-2)$ $y = 2 + 8$ $y = 10$

This matches the value of $y$ in the table.

For $x = -1$, we have:

$y = 2 - 4(-1)$ $y = 2 + 4$ $y = 6$

This matches the value of $y$ in the table.

For $x = 0$, we have:

$y = 2 - 4(0)$ $y = 2 - 0$ $y = 2$

This matches the value of $y$ in the table.

For $x = 1$, we have:

$y = 2 - 4(1)$ $y = 2 - 4$ $y = -2$

This matches the value of $y$ in the table.

For $x = 2$, we have:

$y = 2 - 4(2)$ $y = 2 - 8$ $y = -6$

This matches the value of $y$ in the table.

Conclusion

In conclusion, the table represents the equation $y = 2 - 4x$ accurately. The table provides a visual representation of the equation and helps to illustrate the relationship between the variables. By analyzing the table and verifying the equation, we can see that the table accurately represents the equation.

Properties of the Equation

The equation $y = 2 - 4x$ has several properties that are worth noting.

• Slope: The slope of the equation is $-4$, which means that for every unit increase in $x$, the value of $y$ decreases by $4$ units.
• Y-intercept: The y-intercept of the equation is $2$, which means that the value of $y$ is $2$ when $x = 0$.
• Linearity: The equation is linear, which means that it can be represented by a straight line.
• Domain: The domain of the equation is all real numbers, which means that $x$ can take any value.
• Range: The range of the equation is all real numbers, which means that $y$ can take any value.

Graphing the Equation

The equation $y = 2 - 4x$ can be graphed using a coordinate plane. The graph will be a straight line with a slope of $-4$ and a y-intercept of $2$.

Real-World Applications

The equation $y = 2 - 4x$ has several real-world applications.

• Physics: The equation can be used to model the motion of an object under the influence of gravity.
• Economics: The equation can be used to model the relationship between the price of a good and the quantity demanded.
• Computer Science: The equation can be used to model the relationship between the number of nodes in a graph and the number of edges.

Conclusion

$$$$$$ $$

Q: What is the equation $y = 2 - 4x$?

A: The equation $y = 2 - 4x$ is a linear equation in the form of $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. In this case, the slope is $-4$ and the y-intercept is $2$.

Q: What is the slope of the equation $y = 2 - 4x$?

A: The slope of the equation $y = 2 - 4x$ is $-4$. This means that for every unit increase in $x$, the value of $y$ decreases by $4$ units.

Q: What is the y-intercept of the equation $y = 2 - 4x$?

A: The y-intercept of the equation $y = 2 - 4x$ is $2$. This means that the value of $y$ is $2$ when $x = 0$.

Q: Is the equation $y = 2 - 4x$ linear?

A: Yes, the equation $y = 2 - 4x$ is linear. This means that it can be represented by a straight line.

Q: What is the domain of the equation $y = 2 - 4x$?

A: The domain of the equation $y = 2 - 4x$ is all real numbers. This means that $x$ can take any value.

Q: What is the range of the equation $y = 2 - 4x$?

A: The range of the equation $y = 2 - 4x$ is all real numbers. This means that $y$ can take any value.

Q: How can I graph the equation $y = 2 - 4x$?

A: You can graph the equation $y = 2 - 4x$ using a coordinate plane. The graph will be a straight line with a slope of $-4$ and a y-intercept of $2$.

Q: What are some real-world applications of the equation $y = 2 - 4x$?

A: Some real-world applications of the equation $y = 2 - 4x$ include:

• Physics: The equation can be used to model the motion of an object under the influence of gravity.
• Economics: The equation can be used to model the relationship between the price of a good and the quantity demanded.
• Computer Science: The equation can be used to model the relationship between the number of nodes in a graph and the number of edges.

Q: How can I use the equation $y = 2 - 4x$ in a real-world scenario?

A: You can use the equation $y = 2 - 4x$ in a real-world scenario by substituting the values of $x$ and $y$ into the equation and solving for the unknown variable. For example, if you know the price of a good and the quantity demanded, you can use the equation to model the relationship between the two variables.

Q: What are some common mistakes to avoid when working with the equation $y = 2 - 4x$?

A: Some common mistakes to avoid when working with the equation $y = 2 - 4x$ include:

• Not checking the domain and range of the equation: Make sure to check the domain and range of the equation to ensure that it is valid for the given values of $x$ and $y$.
• Not using the correct slope and y-intercept: Make sure to use the correct slope and y-intercept when graphing the equation.
• Not checking for extraneous solutions: Make sure to check for extraneous solutions when solving the equation.

Q: How can I learn more about the equation $y = 2 - 4x$?

A: You can learn more about the equation $y = 2 - 4x$ by:

• Reading online resources: Read online resources such as textbooks, articles, and websites to learn more about the equation.
• Watching video tutorials: Watch video tutorials to learn more about the equation and how to graph it.
• Practicing problems: Practice problems to learn more about the equation and how to apply it in real-world scenarios.