Question
Which of the following statements is NOT correct about a linear function? A. The equation \( \frac{y}{8}=x \) is an example of a linear function. B. A linear function can be represented by an equation \( y=m x+b \). C. The graph of a linear function is a straight line. D. The equation \( \frac{y}{7}=x^{2} \) is an example of a linear function.
Ask by Hardy Patel. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equation \( \frac{y}{7}=x^{2} \) is **not** an example of a linear function.
Solution
The statement that is **NOT** correct about a linear function is:
**D. The equation \( \frac{y}{7}=x^{2} \) is an example of a linear function.**
**Explanation:**
- **A. \( \frac{y}{8}=x \)**
This equation can be rewritten as \( y = 8x \), which is a linear function because it fits the form \( y = mx + b \) with \( m = 8 \) and \( b = 0 \).
- **B. \( y = mx + b \)**
This is the standard form of a linear function, where \( m \) is the slope and \( b \) is the y-intercept.
- **C. The graph of a linear function is a straight line.**
By definition, the graph of any linear function is a straight line.
- **D. \( \frac{y}{7}=x^{2} \)**
This equation can be rewritten as \( y = 7x^{2} \), which is a quadratic function, not a linear function, because it involves \( x^{2} \), making the graph a parabola rather than a straight line.
**Therefore, the incorrect statement about a linear function is option D.**
**Answer:**
D. The equation \( \frac{y}{7}=x^{2} \) is an example of a linear function.
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Simplify this solution Beyond the Answer
The statement that is NOT correct about a linear function is: D. The equation \( \frac{y}{7}=x^{2} \) is an example of a linear function. This equation represents a quadratic function because of the \( x^{2} \) term, resulting in a parabolic graph rather than a straight line. Linear functions are great for modeling real-world scenarios! For instance, if you’re trying to determine the total cost of a certain number of items at a fixed price each, the relationship can be described with a linear equation like \( y = mx + b \), where \( m \) is the price per item and \( b \) is any fixed fees. This simplistic view helps businesses and individuals forecast expenses easily!
