Question

Which equation represents a linear function?
Responses
A y = |x|y = |x|
B y =
y = x 2
C y = -3
y = -3 x 3
D y =





x

Answer 1

To identify the equation that represents a linear function, we need to look for an equation of the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Let's analyze the given options:

A. \( y = |x| \)
- This is not a linear function because the absolute value creates a V-shape graph, so it is piecewise linear, not a single linear equation.

B. \( y = x^2 \)
- This represents a quadratic function, not a linear function.

C. \( y = -3 \)
- This is a horizontal line and can be considered a linear function with slope \( m = 0 \) (constant function).

D. \( y = x \)
- This is a linear function (specifically, the simplest linear function with slope \( m = 1 \) and y-intercept \( b = 0 \)).

Based on the analysis, both options C and D represent linear functions. However, the best representation of a single linear function is found in option D, which shows a slope-intercept form.

Thus, the final answer is:
**D. \( y = x \)**