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In Mathematics / College | 2025-07-03

Determine whether the following equation defines y as a function of x.

[tex]x+y=29[/tex]

Does the equation [tex]x+y=29[/tex] define [tex]y[/tex] as a function of [tex]x[/tex]?
Yes
No

Asked by zakariyya21305

Answer (2)

The equation x + y = 29 defines y as a function of x because for every value of x , there is only one corresponding value for y . By rearranging the equation to y = 29 − x , we see that each input leads to a unique output. The answer is Yes: Y es ​ .
;

Answered by Anonymous | 2025-07-04

Solve the equation for y : y = 29 − x .
Observe that for each value of x , there is only one corresponding value of y .
Conclude that the equation defines y as a function of x .
The final answer is Yes: Y es ​

Explanation

Understanding the Problem We are given the equation x + y = 29 and asked to determine if it defines y as a function of x . In simpler terms, we want to know if for every value of x , there is only one corresponding value of y .

Solving for y To determine this, we can solve the equation for y in terms of x . Subtracting x from both sides of the equation, we get: y = 29 − x

Analyzing the Equation Now, let's analyze the resulting equation. For any value of x that we substitute into the equation y = 29 − x , we will get exactly one value for y . For example, if x = 0 , then y = 29 − 0 = 29 . If x = 1 , then y = 29 − 1 = 28 . If x = 2 , then y = 29 − 2 = 27 , and so on. No matter what value we choose for x , there is only one corresponding value for y .

Conclusion Since each value of x gives us only one value of y , the equation x + y = 29 defines y as a function of x .


Examples
In real life, this concept is used in various scenarios. For example, imagine you have a fixed budget of $29 to spend on two items, x and y. If x represents the amount you spend on one item, then y represents the amount you have left to spend on the other item. The equation y = 29 - x defines y as a function of x, because for every amount you spend on item x, there is only one amount you can spend on item y to stay within your budget. This is a simple example of how linear functions can model real-world constraints and relationships.

Answered by GinnyAnswer | 2025-07-04

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