Fill In The Table Using This Function Rule:$y = -5x - 1$\[ \begin{array}{|c|c|} \hline x & Y \\ \hline -1 & \square \\ \hline 0 & \square \\ \hline 1 & \square \\ \hline 2 & \square \\ \hline \end{array} \\]
Introduction
In mathematics, linear equations are a fundamental concept that can be used to model various real-world situations. 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 using a function rule and filling in a table with the corresponding values.
The Function Rule
The function rule given is . This means that for every value of x, we can find the corresponding value of y by plugging in the value of x into the equation and solving for y.
Filling in the Table
To fill in the table, we need to substitute the given values of x into the function rule and solve for y.
Substituting x = -1
When x = -1, we substitute this value into the function rule:
Simplifying the equation, we get:
So, when x = -1, y = 4.
Substituting x = 0
When x = 0, we substitute this value into the function rule:
Simplifying the equation, we get:
So, when x = 0, y = -1.
Substituting x = 1
When x = 1, we substitute this value into the function rule:
Simplifying the equation, we get:
So, when x = 1, y = -6.
Substituting x = 2
When x = 2, we substitute this value into the function rule:
Simplifying the equation, we get:
So, when x = 2, y = -11.
The Completed Table
Now that we have filled in the table, it should look like this:
| x | y |
|---|---|
| -1 | 4 |
| 0 | -1 |
| 1 | -6 |
| 2 | -11 |
Conclusion
In this article, we have used a function rule to fill in a table with corresponding values. We have substituted the given values of x into the function rule and solved for y. This is a simple example of how linear equations can be used to model real-world situations. By understanding how to solve linear equations, we can apply this knowledge to a wide range of problems.
Tips and Tricks
- When substituting values into a function rule, make sure to follow the order of operations (PEMDAS).
- When simplifying equations, make sure to combine like terms.
- When solving for y, make sure to isolate the variable y on one side of the equation.
Practice Problems
Try filling in the table using the function rule .
| x | y |
|---|---|
| -2 | |
| 0 | |
| 1 | |
| 2 |
Answer Key
| x | y |
|---|---|
| -2 | -1 |
| 0 | 3 |
| 1 | 5 |
| 2 | 7 |
Q: What is a function rule?
A: A function rule is an equation that describes a relationship between two variables, x and y. It is a way to express how y changes when x changes.
Q: How do I fill in a table using a function rule?
A: To fill in a table using a function rule, you need to substitute the given values of x into the function rule and solve for y. Make sure to follow the order of operations (PEMDAS) and combine like terms when simplifying the equation.
Q: What if I have a negative value for x?
A: If you have a negative value for x, you can still substitute it into the function rule and solve for y. Just remember to follow the order of operations and combine like terms.
Q: Can I use a function rule to model real-world situations?
A: Yes, function rules can be used to model real-world situations. For example, you can use a function rule to describe the relationship between the number of hours worked and the amount of money earned.
Q: How do I know if a function rule is linear or non-linear?
A: A function rule is linear if it can be written in the form y = mx + b, where m is the slope and b is the y-intercept. If the function rule cannot be written in this form, it is non-linear.
Q: What is the difference between a function rule and an equation?
A: A function rule is a specific type of equation that describes a relationship between two variables, x and y. An equation is a statement that says two things are equal, but it may not necessarily describe a relationship between two variables.
Q: Can I use a function rule to solve a system of equations?
A: Yes, you can use a function rule to solve a system of equations. By substituting the values of x and y into the function rule, you can solve for the values of x and y that satisfy both equations.
Q: How do I graph a function rule?
A: To graph a function rule, you can use a table of values to find the corresponding y-values for a given set of x-values. Then, you can plot the points on a coordinate plane and draw a line through them.
Q: What is the significance of the y-intercept in a function rule?
A: The y-intercept is the point where the function rule intersects the y-axis. It represents the value of y when x is equal to zero.
Q: Can I use a function rule to model a quadratic relationship?
A: No, a function rule cannot be used to model a quadratic relationship. Quadratic relationships require a different type of equation, such as y = ax^2 + bx + c.
Q: How do I determine the domain and range of a function rule?
A: To determine the domain and range of a function rule, you need to consider the values of x and y that are possible. The domain is the set of all possible x-values, and the range is the set of all possible y-values.
Q: Can I use a function rule to model a periodic relationship?
A: No, a function rule cannot be used to model a periodic relationship. Periodic relationships require a different type of equation, such as y = sin(x) or y = cos(x).
Conclusion
In this article, we have answered some of the most frequently asked questions about filling in a table using a function rule. We have covered topics such as function rules, linear and non-linear equations, and graphing. We hope this article has been helpful in understanding how to fill in a table using a function rule. If you have any further questions, please don't hesitate to ask.