QQuestionMathematics
QuestionMathematics
# 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.
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