Copy And Complete The Table For The Graph 2 X − Y = 8 2x - Y = 8 2 X − Y = 8 .${ \begin{tabular}{c|c|c|c|c|c} x & -2 & -1 & 0 & 1 & 2 \ \hline y & A & -10 & B & -6 & C \ \end{tabular} }$

Solving Linear Equations: A Step-by-Step Guide to Completing the Table

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving the linear equation $2x - y = 8$ by completing a table. This approach will help us visualize the relationship between the variables $x$ and $y$ and understand how to find the values of $y$ for different values of $x$.

Understanding the Equation

The given equation is $2x - y = 8$. To solve for $y$, we need to isolate the variable $y$ on one side of the equation. We can do this by adding $y$ to both sides of the equation, which gives us:

$$2x = y + 8$$

Next, we can subtract $8$ from both sides of the equation to get:

$$2x - 8 = y$$

This equation tells us that the value of $y$ is equal to $2x - 8$.

Completing the Table

Now that we have the equation $y = 2x - 8$, we can use it to complete the table. We will substitute the values of $x$ from the table into the equation and find the corresponding values of $y$.

x	-2	-1	0	1	2
y	A	-10	B	-6	C

To find the value of $y$ for $x = -2$, we substitute $x = -2$ into the equation $y = 2x - 8$:

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

Simplifying the equation, we get:

$$y = -4 - 8$$

$$y = -12$$

So, the value of $y$ for $x = -2$ is $-12$. We can write this as:

x	-2	-1	0	1	2
y	-12	A	B	-6	C

Next, we will find the value of $y$ for $x = -1$. We substitute $x = -1$ into the equation $y = 2x - 8$:

$$y = 2(-1) - 8$$

Simplifying the equation, we get:

$$y = -2 - 8$$

$$y = -10$$

So, the value of $y$ for $x = -1$ is $-10$. We can write this as:

x	-2	-1	0	1	2
y	-12	-10	B	-6	C

Now, we will find the value of $y$ for $x = 0$. We substitute $x = 0$ into the equation $y = 2x - 8$:

$$y = 2(0) - 8$$

Simplifying the equation, we get:

$$y = 0 - 8$$

$$y = -8$$

So, the value of $y$ for $x = 0$ is $-8$. We can write this as:

x	-2	-1	0	1	2
y	-12	-10	-8	-6	C

Next, we will find the value of $y$ for $x = 1$. We substitute $x = 1$ into the equation $y = 2x - 8$:

$$y = 2(1) - 8$$

Simplifying the equation, we get:

$$y = 2 - 8$$

$$y = -6$$

So, the value of $y$ for $x = 1$ is $-6$. We can write this as:

x	-2	-1	0	1	2
y	-12	-10	-8	-6	C

Finally, we will find the value of $y$ for $x = 2$. We substitute $x = 2$ into the equation $y = 2x - 8$:

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

Simplifying the equation, we get:

$$y = 4 - 8$$

$$y = -4$$

So, the value of $y$ for $x = 2$ is $-4$. We can write this as:

x	-2	-1	0	1	2
y	-12	-10	-8	-6	-4

In this article, we solved the linear equation $2x - y = 8$ by completing a table. We used the equation $y = 2x - 8$ to find the values of $y$ for different values of $x$. By substituting the values of $x$ into the equation, we were able to find the corresponding values of $y$. This approach helped us visualize the relationship between the variables $x$ and $y$ and understand how to solve linear equations.

• When solving linear equations, it's essential to isolate the variable on one side of the equation.
• Use the equation $y = mx + b$ to find the values of $y$ for different values of $x$.
• Substitute the values of $x$ into the equation to find the corresponding values of $y$.
• Use a table to organize the values of $x$ and $y$ and make it easier to visualize the relationship between the variables.

• Solve the linear equation $x + 2y = 6$ by completing a table.
• Find the values of $y$ for $x = -3$, $x = -2$, $x = 0$, $x = 1$, and $x = 2$.
• Use the equation $y = mx + b$ to find the values of $y$ for different values of $x$.

• Linear Equations
• [Completing the Table](https://www.khanacademy.org/math/algebra/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f7d7/x2f6f
  Frequently Asked Questions: Solving Linear Equations

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $ax + by = c$, where $a$, $b$, and $c$ are constants, and $x$ and $y$ are variables.

A: To solve a linear equation, you need to isolate the variable(s) on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

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

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A: To find the values of $y$ for different values of $x$, you can substitute the values of $x$ into the equation $y = mx + b$. This will give you the corresponding values of $y$.

A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2.

A: To solve a system of linear equations, you need to find the values of the variables that satisfy all the equations in the system. You can do this by using substitution or elimination methods.

A: Solving linear equations is an essential skill in mathematics and is used in many real-world applications, such as physics, engineering, economics, and computer science.

A: Yes, here are some examples of linear equations:

• $2x + 3y = 5$
• $x - 2y = 3$
• $y = 2x - 1$
• $x + y = 4$

A: Yes, here are some tips for solving linear equations:

• Make sure to isolate the variable(s) on one side of the equation.
• Use the equation $y = mx + b$ to find the values of $y$ for different values of $x$.
• Substitute the values of $x$ into the equation to find the corresponding values of $y$.
• Use a table to organize the values of $x$ and $y$ and make it easier to visualize the relationship between the variables.

A: Yes, here are some practice problems for solving linear equations:

• Solve the linear equation $x + 2y = 6$ by completing a table.
• Find the values of $y$ for $x = -3$, $x = -2$, $x = 0$, $x = 1$, and $x = 2$.
• Use the equation $y = mx + b$ to find the values of $y$ for different values of $x$.

In this article, we have discussed the basics of solving linear equations, including the equation $y = mx + b$, and provided some tips and practice problems for solving linear equations. We hope that this article has been helpful in understanding the concept of solving linear equations and has provided you with the skills and confidence to solve linear equations on your own.