Use The Equation $2m + 4s = 16$ To Complete The Table, Then Graph The Line Using $s$ As The Dependent Variable.$\[ \begin{array}{|c|c|} \hline m & S \\ \hline -2 & \\ 3 & \\ 0 & \\ \hline \end{array} \\]

Feb 26, 2025 by ADMIN 204 views

Introduction

In mathematics, solving linear equations and graphing lines are fundamental concepts that are used extensively in various fields, including algebra, geometry, and calculus. In this article, we will focus on using the equation $2m + 4s = 16$ to complete a table and then graph the line using $s$ as the dependent variable.

Understanding the Equation

The given equation is a linear equation in two variables, $m$ and $s$ . The equation is $2m + 4s = 16$ . To solve for $s$ , we need to isolate the variable $s$ on one side of the equation. We can do this by subtracting $2m$ from both sides of the equation and then dividing both sides by $4$ .

Completing the Table

To complete the table, we need to find the values of $s$ for the given values of $m$ . We can do this by substituting the values of $m$ into the equation and solving for $s$ .

m	s
-2
3
0

Let's start by substituting $m = -2$ into the equation:

$2(-2) + 4s = 16$

$-4 + 4s = 16$

$4s = 20$

$s = 5$

So, the value of $s$ for $m = -2$ is $5$ .

Next, let's substitute $m = 3$ into the equation:

$2(3) + 4s = 16$

$6 + 4s = 16$

$4s = 10$

$s = 2.5$

So, the value of $s$ for $m = 3$ is $2.5$ .

Finally, let's substitute $m = 0$ into the equation:

$2(0) + 4s = 16$

$0 + 4s = 16$

$4s = 16$

$s = 4$

So, the value of $s$ for $m = 0$ is $4$ .

Completed Table

m	s
-2	5
3	2.5
0	4

Graphing the Line

To graph the line, we need to plot the points $(m, s)$ for each value of $m$ in the table. We can do this by using a coordinate plane and plotting the points $(m, s)$ for each value of $m$ .

Plotting the Points

Let's start by plotting the point $(-2, 5)$ :

The x-coordinate is $-2$ , so we plot a point $2$ units to the left of the y-axis.
The y-coordinate is $5$ , so we plot a point $5$ units above the x-axis.

Next, let's plot the point $(3, 2.5)$ :

The x-coordinate is $3$ , so we plot a point $3$ units to the right of the y-axis.
The y-coordinate is $2.5$ , so we plot a point $2.5$ units above the x-axis.

Finally, let's plot the point $(0, 4)$ :

The x-coordinate is $0$ , so we plot a point on the y-axis.
The y-coordinate is $4$ , so we plot a point $4$ units above the x-axis.

Graphing the Line

To graph the line, we need to connect the points $(m, s)$ for each value of $m$ in the table. We can do this by drawing a line through the points $(m, s)$ for each value of $m$ .

Conclusion

In this article, we used the equation $2m + 4s = 16$ to complete a table and then graph the line using $s$ as the dependent variable. We found the values of $s$ for the given values of $m$ and plotted the points $(m, s)$ for each value of $m$ . We then connected the points to graph the line. This article demonstrates the importance of solving linear equations and graphing lines in mathematics.

References

[1] "Linear Equations and Graphs" by Math Open Reference
[2] "Solving Linear Equations" by Khan Academy
[3] "Graphing Lines" by Purplemath

Discussion

What are some real-world applications of solving linear equations and graphing lines?
How can you use technology to graph lines and solve linear equations?
What are some common mistakes to avoid when solving linear equations and graphing lines?

Additional Resources

[1] "Linear Equations and Graphs" by Math Open Reference
[2] "Solving Linear Equations" by Khan Academy
[3] "Graphing Lines" by Purplemath

Final Thoughts

Introduction

In our previous article, we discussed how to solve linear equations and graph lines using the equation $2m + 4s = 16$ . We completed a table and graphed the line using $s$ as the dependent variable. In this article, we will answer some frequently asked questions about solving linear equations and graphing lines.

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 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.

Q: What is the difference between a dependent variable and an independent variable?

A: In a linear equation, the dependent variable is the variable that is being solved for, while the independent variable is the variable that is being used to solve for the dependent variable.

Q: How do I graph a line?

A: To graph a line, you need to plot the points $(x, y)$ for each value of $x$ in the equation. You can do this by using a coordinate plane and plotting the points $(x, y)$ for each value of $x$ .

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

A: The equation of a line in slope-intercept form 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 line?

A: To find the slope of a line, you need to use the 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 line?

A: The y-intercept of a line is the point where the line intersects the y-axis. It is the value of $y$ when $x = 0$ .

Q: How do I graph a line using a table?

A: To graph a line using a table, you need to create a table with the values of $x$ and $y$ for each point on the line. You can then plot the points $(x, y)$ for each value of $x$ .

Q: What are some common mistakes to avoid when solving linear equations and graphing lines?

A: Some common mistakes to avoid when solving linear equations and graphing lines include:

Not isolating the variable(s) on one side of the equation
Not using the correct formula for the slope of a line
Not plotting the points $(x, y)$ for each value of $x$
Not using a coordinate plane to graph the line

Conclusion

Solving linear equations and graphing lines are fundamental concepts in mathematics that have numerous real-world applications. By understanding how to solve linear equations and graph lines, you can apply these concepts to a wide range of fields, including science, engineering, and economics. This article answers some frequently asked questions about solving linear equations and graphing lines, providing a step-by-step guide on how to complete a table and graph a line using $s$ as the dependent variable.

References

[1] "Linear Equations and Graphs" by Math Open Reference
[2] "Solving Linear Equations" by Khan Academy
[3] "Graphing Lines" by Purplemath

Discussion

What are some real-world applications of solving linear equations and graphing lines?
How can you use technology to graph lines and solve linear equations?
What are some common mistakes to avoid when solving linear equations and graphing lines?

Additional Resources

[1] "Linear Equations and Graphs" by Math Open Reference
[2] "Solving Linear Equations" by Khan Academy
[3] "Graphing Lines" by Purplemath

Final Thoughts

Solving linear equations and graphing lines are fundamental concepts in mathematics that have numerous real-world applications. By understanding how to solve linear equations and graph lines, you can apply these concepts to a wide range of fields, including science, engineering, and economics. This article provides a step-by-step guide on how to complete a table and graph a line using $s$ as the dependent variable, and answers some frequently asked questions about solving linear equations and graphing lines.