Question
Which equation represents a linear function?
Responses
A y = |x|
B y = x^(2)
C y = -3x^(3)
D y = 1 over 4 x
Responses
A y = |x|
B y = x^(2)
C y = -3x^(3)
D y = 1 over 4 x
Answers
GPT-4o mini
A linear function can be expressed in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Let's analyze each option:
A. \( y = |x| \) - This is not a linear function; it has a V-shape due to the absolute value.
B. \( y = x^{2} \) - This is a quadratic function, not linear.
C. \( y = -3x^{3} \) - This is a cubic function, not linear.
D. \( y = \frac{1}{4} x \) - This is in the form of \( y = mx + b \) with \( m = \frac{1}{4} \) and \( b = 0 \), making it a linear function.
Therefore, the correct response that represents a linear function is:
**D. \( y = \frac{1}{4} x \)**
Let's analyze each option:
A. \( y = |x| \) - This is not a linear function; it has a V-shape due to the absolute value.
B. \( y = x^{2} \) - This is a quadratic function, not linear.
C. \( y = -3x^{3} \) - This is a cubic function, not linear.
D. \( y = \frac{1}{4} x \) - This is in the form of \( y = mx + b \) with \( m = \frac{1}{4} \) and \( b = 0 \), making it a linear function.
Therefore, the correct response that represents a linear function is:
**D. \( y = \frac{1}{4} x \)**