QQuestionMathematics
QuestionMathematics
Determine whether the following equation represents a linear or non-linear function. Provide steps if possible.
2x+ 3y= 9xy
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Answer
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Step 1:: Identify the given equation.
The given equation is $2x + 3y = 9xy$.
Step 2:: Understand the difference between linear and non-linear functions.
A linear function has a degree of 1, meaning the highest power of the variable(s) in the function is 1. A non-linear function has a degree greater than 1, meaning the highest power of the variable(s) in the function is greater than 1.
Step 3:: Examine the given equation for the degree.
This indicates that the equation does not represent a simple sum of terms with only $x$ and $y$ but also their product $xy$.
Consequently, the degree of the equation cannot be 1, and the equation does not represent a linear function.
Step 4:: Confirm the non-linearity of the function.
However, we have already determined that the equation does not represent a linear function due to the presence of the $xy$ term.
Since this equation does not fit the standard form of a second-degree polynomial, it is not a quadratic function either. Therefore, we can conclude that the given equation represents a non-linear function.
Final Answer
The given equation $2x + 3y = 9xy$ represents a non-linear function.
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