Importance of Linear Functions

Oct 13, 2025 by miodeya.com 128 views

Understanding the Function

The given function is $y = 8 - 2x$ . This is a linear function, where the value of $y$ is determined by the value of $x$ . The function has a slope of -2, which means that for every increase in $x$ by 1, the value of $y$ decreases by 2.

Analyzing the Table

The table shows ordered pairs of the function, where each pair consists of a value of $x$ and the corresponding value of $y$ . By examining the table, we can see that the function is indeed linear, with a consistent slope of -2.

x	y
-3	14
-1	10
1	6
4	0
8	?

Finding the Value of $y$

To find the value of $y$ when $x = 8$ , we can use the function $y = 8 - 2x$ . We simply substitute $x = 8$ into the function and solve for $y$ .

$y = 8 - 2(8)$

$y = 8 - 16$

$y = -8$

Therefore, the value of $y$ when $x = 8$ is -8.

Conclusion

Importance of Linear Functions

Linear functions are an important concept in mathematics, as they can be used to model real-world situations. For example, a linear function can be used to model the cost of a product based on the number of units sold. In this case, the cost of the product would increase or decrease linearly with the number of units sold.

Real-World Applications

Linear functions have many real-world applications, including:

Cost analysis: Linear functions can be used to model the cost of a product based on the number of units sold.
Supply and demand: Linear functions can be used to model the supply and demand of a product in a market.
Distance and speed: Linear functions can be used to model the distance traveled by an object based on its speed.
Finance: Linear functions can be used to model the growth of an investment over time.

Tips for Solving Linear Functions

When solving linear functions, it is often helpful to use the following tips:

Use the slope-intercept form: The slope-intercept form of a linear function is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
Use the table of values: A table of values can be used to help visualize the function and find the value of $y$ for a given value of $x$ .
Substitute values into the function: To find the value of $y$ for a given value of $x$ , simply substitute the value of $x$ into the function and solve for $y$ .

Conclusion

In conclusion, we have analyzed the given function $y = 8 - 2x$ and used the table of ordered pairs to find the value of $y$ when $x = 8$ . By substituting $x = 8$ into the function, we found that the value of $y$ is -8. We have also discussed the importance of linear functions and provided tips for solving linear functions.

Q&A: Understanding the Function

Q: What is the slope of the function $y = 8 - 2x$ ?

A: The slope of the function $y = 8 - 2x$ is -2. This means that for every increase in $x$ by 1, the value of $y$ decreases by 2.

Q: What is the y-intercept of the function $y = 8 - 2x$ ?

A: The y-intercept of the function $y = 8 - 2x$ is 8. This means that when $x = 0$ , the value of $y$ is 8.

Q: How can I use the table of ordered pairs to find the value of $y$ for a given value of $x$ ?

A: To use the table of ordered pairs to find the value of $y$ for a given value of $x$ , simply look up the value of $x$ in the table and find the corresponding value of $y$ .

Q: Can I use the function $y = 8 - 2x$ to model real-world situations?

A: Yes, the function $y = 8 - 2x$ can be used to model real-world situations. For example, a linear function can be used to model the cost of a product based on the number of units sold.

Q: What are some real-world applications of linear functions?

A: Some real-world applications of linear functions include:

Cost analysis: Linear functions can be used to model the cost of a product based on the number of units sold.
Supply and demand: Linear functions can be used to model the supply and demand of a product in a market.
Distance and speed: Linear functions can be used to model the distance traveled by an object based on its speed.
Finance: Linear functions can be used to model the growth of an investment over time.

Q: How can I solve linear functions?

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

Use the slope-intercept form: The slope-intercept form of a linear function is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
Use the table of values: A table of values can be used to help visualize the function and find the value of $y$ for a given value of $x$ .
Substitute values into the function: To find the value of $y$ for a given value of $x$ , simply substitute the value of $x$ into the function and solve for $y$ .

Q: What are some tips for working with linear functions?

A: Some tips for working with linear functions include:

Use the slope-intercept form: The slope-intercept form of a linear function is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
Use the table of values: A table of values can be used to help visualize the function and find the value of $y$ for a given value of $x$ .
Substitute values into the function: To find the value of $y$ for a given value of $x$ , simply substitute the value of $x$ into the function and solve for $y$ .

Conclusion

In conclusion, we have provided a Q&A article to help you understand the function $y = 8 - 2x$ and how to use it to model real-world situations. We have also provided tips for solving linear functions and working with linear functions.