Fill In The Table Using The Equation \[$ Y = 4x - 6 \$\].$\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline & \\ \hline & \\ \hline & \\ \hline & \\ \hline & \\ \hline &

Introduction

In mathematics, linear equations are a fundamental concept that helps us understand the relationship between variables. A linear equation is an equation in which the highest power of the variable(s) is 1. In this article, we will focus on solving linear equations using the equation $y = 4x - 6$. We will use this equation to fill in a table with different values of $x$ and calculate the corresponding values of $y$.

The Equation

The given equation is $y = 4x - 6$. This equation represents a linear relationship between the variables $x$ and $y$. The coefficient of $x$ is 4, which means that for every unit increase in $x$, the value of $y$ increases by 4 units. The constant term is -6, which means that when $x$ is 0, the value of $y$ is -6.

Filling in the Table

We will use the equation $y = 4x - 6$ to fill in the table with different values of $x$ and calculate the corresponding values of $y$.

Step 1: Fill in the table with x = 0

When $x$ is 0, we can substitute this value into the equation to find the corresponding value of $y$.

$$y = 4(0) - 6$$

$$y = -6$$

So, when $x$ is 0, the value of $y$ is -6.

Step 2: Fill in the table with x = 1

When $x$ is 1, we can substitute this value into the equation to find the corresponding value of $y$.

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

$$y = -2$$

So, when $x$ is 1, the value of $y$ is -2.

Step 3: Fill in the table with x = 2

When $x$ is 2, we can substitute this value into the equation to find the corresponding value of $y$.

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

$$y = 2$$

So, when $x$ is 2, the value of $y$ is 2.

Step 4: Fill in the table with x = 3

When $x$ is 3, we can substitute this value into the equation to find the corresponding value of $y$.

$$y = 4(3) - 6$$

$$y = 12$$

So, when $x$ is 3, the value of $y$ is 12.

Step 5: Fill in the table with x = 4

When $x$ is 4, we can substitute this value into the equation to find the corresponding value of $y$.

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

$$y = 14$$

So, when $x$ is 4, the value of $y$ is 14.

Step 6: Fill in the table with x = 5

When $x$ is 5, we can substitute this value into the equation to find the corresponding value of $y$.

$$y = 4(5) - 6$$

$$y = 16$$

So, when $x$ is 5, the value of $y$ is 16.

Conclusion

In this article, we used the equation $y = 4x - 6$ to fill in a table with different values of $x$ and calculated the corresponding values of $y$. We saw that for every unit increase in $x$, the value of $y$ increases by 4 units. The constant term -6 means that when $x$ is 0, the value of $y$ is -6. We can use this equation to solve linear equations and understand the relationship between variables.

Table

$x$	$y$
0	-6
1	-2
2	2
3	12
4	14
5	16

Discussion

This equation can be used to model real-world situations, such as the cost of producing a product or the revenue generated by a business. The equation can be used to predict the value of $y$ for a given value of $x$. The table can be used to visualize the relationship between $x$ and $y$ and to identify patterns or trends.

Applications

This equation has many applications in mathematics, science, and engineering. It can be used to solve linear equations, graph linear functions, and model real-world situations. The equation can be used to predict the value of $y$ for a given value of $x$ and to identify patterns or trends.

Limitations

This equation has some limitations. It is a linear equation, which means that it can only model linear relationships between variables. It cannot be used to model non-linear relationships between variables. Additionally, the equation assumes that the relationship between $x$ and $y$ is constant, which may not always be the case in real-world situations.

Future Work

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Q: What is the equation $y = 4x - 6$ used for?

A: The equation $y = 4x - 6$ is used to model linear relationships between variables. It can be used to solve linear equations, graph linear functions, and predict the value of $y$ for a given value of $x$.

Q: How do I use the equation $y = 4x - 6$ to solve a linear equation?

A: To use the equation $y = 4x - 6$ to solve a linear equation, simply substitute the given values of $x$ and $y$ into the equation and solve for the unknown variable.

Q: What is the significance of the coefficient 4 in the equation $y = 4x - 6$?

A: The coefficient 4 in the equation $y = 4x - 6$ represents the rate of change of $y$ with respect to $x$. It means that for every unit increase in $x$, the value of $y$ increases by 4 units.

Q: What is the significance of the constant term -6 in the equation $y = 4x - 6$?

A: The constant term -6 in the equation $y = 4x - 6$ represents the value of $y$ when $x$ is 0. It means that when $x$ is 0, the value of $y$ is -6.

Q: Can I use the equation $y = 4x - 6$ to model non-linear relationships between variables?

A: No, the equation $y = 4x - 6$ is a linear equation and can only be used to model linear relationships between variables. It cannot be used to model non-linear relationships between variables.

Q: How do I graph the equation $y = 4x - 6$?

A: To graph the equation $y = 4x - 6$, simply plot the points $(0, -6)$, $(1, -2)$, $(2, 2)$, $(3, 12)$, $(4, 14)$, and $(5, 16)$ on a coordinate plane and draw a line through them.

Q: Can I use the equation $y = 4x - 6$ to make predictions about future values of $y$?

A: Yes, the equation $y = 4x - 6$ can be used to make predictions about future values of $y$. Simply substitute the given value of $x$ into the equation and solve for $y$.

Q: What are some real-world applications of the equation $y = 4x - 6$?

A: Some real-world applications of the equation $y = 4x - 6$ include modeling the cost of producing a product, predicting the revenue generated by a business, and understanding the relationship between variables in a scientific experiment.

Q: Can I use the equation $y = 4x - 6$ to solve systems of linear equations?

A: Yes, the equation $y = 4x - 6$ can be used to solve systems of linear equations. Simply substitute the given values of $x$ and $y$ into the equation and solve for the unknown variable.

Conclusion

In this article, we have answered some frequently asked questions about the equation $y = 4x - 6$. We have discussed its significance, how to use it to solve linear equations, and its real-world applications. We have also provided some examples of how to use the equation to make predictions about future values of $y$.