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# Which equation represents a linear function? Equation 1: $y= 2 x^{2}+ 1$ Equation 2: $y^{2}= 3 x+ 1$ Equation 3: $y= 5 x- 1$ Equation 4: $y= 4 x^{4}- 1$ A. Equation 1 B. Equation 2 C. Equation 3 D. Equation 4
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Answer

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Step 1:
I'll solve this step by step, carefully following the LaTeX formatting guidelines:

Step 2:
: Recall the definition of a linear function

- The equation has a first-degree (linear) term in $$x
- m is the slope of the line

Step 3:
: Examine Equation 1

y = 2x^{2} + 1
- Contains a quadratic term x^{2} - NOT a linear function

Step 4:
: Examine Equation 2

- Has $$y^{2}$$ on the left side
- The equation is not in the form y = mx + b - NOT a linear function

Step 5:
: Examine Equation 3

- $$b = -1$$ (y-intercept)
- Matches the linear function form y = mx + b - IS a linear function

Step 6:
: Examine Equation 4

y = 4x^{4} - 1
- Contains a fourth-degree term x^{4} - NOT a linear function

Final Answer

Equation 3 represents a linear function.