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

Feb 26, 2025 by ADMIN 175 views

**Solving Linear Equations and Graphing Lines**

Introduction

In mathematics, linear equations are a fundamental concept that plays a crucial role in various fields, including algebra, geometry, and calculus. 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 a linear equation and graphing a line using the equation $2m + 4s = 16$ . We will also explore the concept of dependent and independent variables.

Understanding the Equation

The given equation is $2m + 4s = 16$ . To solve for the variable $s$ , we need to isolate it on one side of the equation. We can do this by subtracting $2m$ from both sides of the equation, which gives us $4s = 16 - 2m$ . Dividing both sides by 4, we get $s = \frac{16 - 2m}{4}$ .

Simplifying the Equation

We can simplify the equation further by dividing both the numerator and the denominator by 2, which gives us $s = \frac{8 - m}{2}$ .

Completing the Table

To complete the table, we need to find the values of $m$ and $s$ that satisfy the equation. We can do this by plugging in different values of $m$ and solving for $s$ . Let's start by plugging in $m = 0$ .

| m | s |
| --- | --- |
| 0 | 4 |

As we can see, when $m = 0$ , $s = 4$ . Now, let's plug in $m = 1$ .

| m | s |
| --- | --- |
| 0 | 4 |
| 1 | 3 |

When $m = 1$ , $s = 3$ . We can continue this process by plugging in different values of $m$ and solving for $s$ .

| m | s |
| --- | --- |
| 0 | 4 |
| 1 | 3 |
| 2 | 2 |
| 3 | 1 |
| 4 | 0 |

Graphing the Line

Now that we have completed the table, we can graph the line using $s$ as the dependent variable. To do this, we need to plot the points on a coordinate plane and draw a line through them.

+---------------+
|             |
|  (0, 4)     |
|  (1, 3)     |
|  (2, 2)     |
|  (3, 1)     |
|  (4, 0)     |
|             |
+---------------+

As we can see, the line passes through the points (0, 4), (1, 3), (2, 2), (3, 1), and (4, 0). We can draw a line through these points to represent the equation $s = \frac{8 - m}{2}$ .

Conclusion

In this article, we solved a linear equation and graphed a line using the equation $2m + 4s = 16$ . We also explored the concept of dependent and independent variables. By completing the table and graphing the line, we were able to visualize the relationship between the variables $m$ and $s$ . This is a fundamental concept in mathematics that has numerous applications in various fields.

Discussion

What is the difference between a dependent and independent variable?
How do you solve a linear equation?
What is the significance of graphing a line in mathematics?

Answer Key

A dependent variable is a variable that depends on the value of another variable, while an independent variable is a variable that is not dependent on the value of another variable.
To solve a linear equation, you need to isolate the variable on one side of the equation.
Graphing a line is significant in mathematics because it allows us to visualize the relationship between variables and make predictions about the behavior of the line.

References

[1] "Linear Equations" by Khan Academy
[2] "Graphing Lines" by Math Open Reference
[3] "Dependent and Independent Variables" by IXL

Additional Resources

[1] "Linear Equations" by Wolfram Alpha
[2] "Graphing Lines" by GeoGebra
[3] "Dependent and Independent Variables" by CK-12
Q&A: Linear Equations and Graphing Lines =============================================

Introduction

In our previous article, we explored the concept of linear equations and graphing lines using the equation $2m + 4s = 16$ . We also discussed the importance of understanding the relationship between dependent and independent variables. In this article, we will answer some frequently asked questions about linear equations and graphing lines.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. It 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 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 and independent variable?

A: A dependent variable is a variable that depends on the value of another variable, while an independent variable is a variable that is not dependent on the value of another variable.

Q: How do I graph a line?

A: To graph a line, you need to plot the points on a coordinate plane and draw a line through them. You can use the equation of the line to find the x and y intercepts, and then plot the points.

Q: What is the significance of graphing a line in mathematics?

A: Graphing a line is significant in mathematics because it allows us to visualize the relationship between variables and make predictions about the behavior of the line.

Q: Can I use a graphing calculator to graph a line?

A: Yes, you can use a graphing calculator to graph a line. Graphing calculators can plot points and draw lines, making it easier to visualize the relationship between variables.

Q: How do I determine the slope of a line?

A: To determine the slope of a line, you need to find the ratio of the vertical change to the horizontal change between two points on the line.

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: Can I use a linear equation to model real-world situations?

A: Yes, you can use a linear equation to model real-world situations. Linear equations can be used to model relationships between variables, such as the cost of goods, the distance traveled, or the amount of money earned.

Q: How do I determine the x and y intercepts of a line?

A: To determine the x and y intercepts of a line, you need to set the other variable equal to zero and solve for the remaining variable.

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.