Complete The Table For The Equation $x + 2y = 8$, And Graph The Equation.$\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 0 & 4 \\ \hline 8 & 0 \\ \hline 6 & 1 \\ \hline $\square$ & 8 \\ \hline \end{tabular} \\]

Introduction

Linear equations are a fundamental concept in mathematics, and they play a crucial role in various fields such as physics, engineering, and economics. In this article, we will focus on solving and graphing linear equations, specifically the equation $x + 2y = 8$. We will complete the table for the given equation and graph the equation to visualize its behavior.

Understanding Linear Equations

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. The graph of a linear equation is a straight line.

Completing the Table

To complete the table for the equation $x + 2y = 8$, we need to find the values of $x$ and $y$ that satisfy the equation. We can do this by substituting different values of $x$ and solving for $y$.

$x$	$y$
0	4
8	0
6	1
$\square$	8

Let's start by substituting $x = 0$ into the equation:

$x + 2y = 8$

$0 + 2y = 8$

$2y = 8$

$y = 4$

So, the first row of the table is complete:

$x$	$y$
0	4

Next, let's substitute $x = 8$ into the equation:

$x + 2y = 8$

$8 + 2y = 8$

$2y = 0$

$y = 0$

So, the second row of the table is complete:

$x$	$y$
0	4
8	0

Now, let's substitute $x = 6$ into the equation:

$x + 2y = 8$

$6 + 2y = 8$

$2y = 2$

$y = 1$

So, the third row of the table is complete:

$x$	$y$
0	4
8	0
6	1

Finally, let's substitute $x = \square$ into the equation and solve for $y$:

$x + 2y = 8$

$\square + 2y = 8$

$2y = 8 - \square$

$y = \frac{8 - \square}{2}$

So, the fourth row of the table is complete:

$x$	$y$
0	4
8	0
6	1
$\square$	$\frac{8 - \square}{2}$

Graphing the Equation

To graph the equation $x + 2y = 8$, we can use the points in the table to plot the line. We will start by plotting the points $(0, 4)$, $(8, 0)$, and $(6, 1)$.

• Plot the point $(0, 4)$ on the coordinate plane.
• Plot the point $(8, 0)$ on the coordinate plane.
• Plot the point $(6, 1)$ on the coordinate plane.

Next, we will draw a line through the points to visualize the graph of the equation.

Conclusion

In this article, we completed the table for the equation $x + 2y = 8$ and graphed the equation to visualize its behavior. We learned how to substitute different values of $x$ into the equation and solve for $y$ to complete the table. We also learned how to plot the points on the coordinate plane and draw a line through the points to visualize the graph of the equation.

Final Answer

The completed table for the equation $x + 2y = 8$ is:

$x$	$y$
0	4
8	0
6	1
$\square$	$\frac{8 - \square}{2}$

The graph of the equation $x + 2y = 8$ is a straight line that passes through the points $(0, 4)$, $(8, 0)$, and $(6, 1)$.

References

• Linear Equations
• Graphing Linear Equations

Further Reading

• Solving Linear Equations
• Graphing Linear Equations

Mathematics Discussion

• Linear Equations
• Graphing Linear Equations

Mathematics Resources

• Khan Academy
• Mathway
• Wolfram Alpha
  Solving and Graphing Linear Equations: A Q&A Guide =====================================================

Introduction

In our previous article, we explored the concept of linear equations and how to solve and graph them. In this article, we will continue to delve deeper into the world of linear equations and answer some of the most frequently asked questions about them.

Q&A

Q: What is a linear equation?

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.

Q: How do I solve a linear equation?

A: To solve a linear equation, you can use the following steps:

1. Isolate the variable(s) on one side of the equation.
2. Use inverse operations to eliminate the coefficients of the variable(s).
3. Simplify the equation to find the value of the variable(s).

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

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. In other words, a linear equation can be written in the form $ax + by = c$, while a quadratic equation can be written in the form $ax^2 + bx + c = 0$.

Q: How do I graph a linear equation?

A: To graph a linear equation, you can use the following steps:

1. Find two points on the line by substituting different values of $x$ and solving for $y$.
2. Plot the points on the coordinate plane.
3. Draw a line through the points to visualize the graph of the equation.

Q: What is the slope-intercept form of a linear equation?

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

Q: How do I find the slope of a linear equation?

A: To find the slope of a linear equation, you can use the following formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.

Q: What is the y-intercept of a linear equation?

A: The y-intercept of a linear equation is the point where the line intersects the y-axis. It is denoted by the symbol $b$ in the slope-intercept form of the equation.

Q: How do I find the y-intercept of a linear equation?

A: To find the y-intercept of a linear equation, you can set $x = 0$ in the equation and solve for $y$.

Q: What is the x-intercept of a linear equation?

A: The x-intercept of a linear equation is the point where the line intersects the x-axis. It is denoted by the symbol $a$ in the equation $ax + by = c$.

Q: How do I find the x-intercept of a linear equation?

A: To find the x-intercept of a linear equation, you can set $y = 0$ in the equation and solve for $x$.

Conclusion

In this article, we answered some of the most frequently asked questions about linear equations. We covered topics such as solving linear equations, graphing linear equations, and finding the slope and y-intercept of a linear equation. We hope that this article has been helpful in clarifying any confusion you may have had about linear equations.

Final Answer

The final answer to the question "What is a linear equation?" is:

A linear equation is an equation in which the highest power of the variable(s) is 1.

References

• Linear Equations
• Graphing Linear Equations
• Slope-Intercept Form

Further Reading

• Solving Linear Equations
• Graphing Linear Equations
• Slope-Intercept Form

Mathematics Discussion

• Linear Equations
• Graphing Linear Equations
• Slope-Intercept Form

Mathematics Resources

• Khan Academy
• Mathway
• Wolfram Alpha