Complete The Table Using The Equation $r = 4k + 1$.$\[ \begin{tabular}{|c|c|} \hline $k$ & $r$ \\ \hline 2 & $\square$ \\ \hline 5 & $\square$ \\ \hline 7 & $\square$ \\ \hline 8 & $\square$ \\ \hline \end{tabular} \\]
Solving for r: A Step-by-Step Guide to Completing the Table
In mathematics, equations are used to represent relationships between variables. One common type of equation is a linear equation, which is in the form of ax + b = c, where a, b, and c are constants. In this article, we will be working with a linear equation in the form of r = 4k + 1, where r and k are variables. Our goal is to complete a table using this equation by finding the values of r for different values of k.
The equation r = 4k + 1 is a linear equation, where r is the dependent variable and k is the independent variable. This means that for every value of k, there is a corresponding value of r. To find the value of r, we simply need to plug in the value of k into the equation and solve for r.
Now that we understand the equation, let's complete the table using the values of k given in the table.
k = 2
To find the value of r when k = 2, we plug in k = 2 into the equation r = 4k + 1.
r = 4(2) + 1
r = 8 + 1
r = 9
So, when k = 2, the value of r is 9.
k = 5
To find the value of r when k = 5, we plug in k = 5 into the equation r = 4k + 1.
r = 4(5) + 1
r = 20 + 1
r = 21
So, when k = 5, the value of r is 21.
k = 7
To find the value of r when k = 7, we plug in k = 7 into the equation r = 4k + 1.
r = 4(7) + 1
r = 28 + 1
r = 29
So, when k = 7, the value of r is 29.
k = 8
To find the value of r when k = 8, we plug in k = 8 into the equation r = 4k + 1.
r = 4(8) + 1
r = 32 + 1
r = 33
So, when k = 8, the value of r is 33.
In this article, we used the equation r = 4k + 1 to complete a table with different values of k. We found the values of r for k = 2, 5, 7, and 8, and filled in the corresponding values in the table. This exercise demonstrates the importance of understanding and applying linear equations in mathematics.
| k | r |
|---|---|
| 2 | 9 |
| 5 | 21 |
| 7 | 29 |
| 8 | 33 |
Linear equations are a fundamental concept in mathematics, and understanding how to apply them is crucial for solving problems in various fields. By following the steps outlined in this article, you can easily complete tables using linear equations and develop a deeper understanding of mathematical concepts.
Frequently Asked Questions: Completing the Table using the Equation r = 4k + 1
In our previous article, we explored the equation r = 4k + 1 and completed a table using this equation. However, we understand that there may be some questions and concerns that readers may have. In this article, we will address some of the most frequently asked questions related to completing the table using the equation r = 4k + 1.
A: The equation r = 4k + 1 is a linear equation, where r is the dependent variable and k is the independent variable. This equation represents a relationship between r and k, where r is equal to 4 times k plus 1.
A: To complete the table using the equation r = 4k + 1, you need to plug in the values of k into the equation and solve for r. For example, if k = 2, you would plug in k = 2 into the equation and solve for r.
A: If you get a negative value for r, it means that the value of k is too small to produce a positive value for r. In this case, you can try plugging in a larger value of k to see if you get a positive value for r.
A: Yes, you can use the equation r = 4k + 1 to solve for k. To do this, you need to isolate k on one side of the equation. For example, if r = 21, you can plug in r = 21 into the equation and solve for k.
A: To determine if the equation r = 4k + 1 is true or false, you need to test it with different values of k. If the equation holds true for all values of k, then it is a valid equation.
A: Yes, you can use the equation r = 4k + 1 to solve real-world problems. For example, if you are a manager and you want to determine the total cost of producing a certain number of items, you can use the equation r = 4k + 1 to calculate the total cost.
A: Some common mistakes to avoid when completing the table using the equation r = 4k + 1 include:
- Plugging in the wrong value of k
- Not solving for r correctly
- Not checking the equation for validity
- Not using the correct units
In this article, we addressed some of the most frequently asked questions related to completing the table using the equation r = 4k + 1. We hope that this article has provided you with a better understanding of the equation and how to use it to solve problems. If you have any further questions or concerns, please don't hesitate to ask.
If you want to learn more about the equation r = 4k + 1, we recommend checking out the following resources:
- Khan Academy: Linear Equations
- Mathway: Linear Equations
- Wolfram Alpha: Linear Equations
Completing the table using the equation r = 4k + 1 is a fundamental concept in mathematics, and understanding how to apply it is crucial for solving problems in various fields. By following the steps outlined in this article and avoiding common mistakes, you can become proficient in using the equation r = 4k + 1 to solve problems.