Question

Which equation represents a linear function?

Which equation represents a linear function?

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Answer

  • Answer

Concepts

Linear functions, degree of a polynomial, identifying linear equations.

Explanation

A linear function is a function that can be written in the form: y=mx+b where m and b are constants, and x is the variable. The key characteristic of a linear function is that the highest power of x (the degree of the polynomial) is 1.

Let us analyze each option:

  1. y=x3: The highest power of x is 3, so this is not a linear function.
  2. y=−3x2+2: The highest power of x is 2, so this is not a linear function.
  3. y=2x2: The highest power of x is 2, so this is not a linear function.
  4. y=−4x+5: The highest power of x is 1, so this is a linear function.

Solution

The equation y=−4x+5 represents a linear function because it is in the form y=mx+b, where m=−4 and b=5.

Final Answer

The equation that represents a linear function is: y=−4x+5

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