Question

Which functions are linear?
Responses
A y = x − 2y = x − 2
B y =


+ 2y = 3 x + 2
C y =


x + 8y = 1 2 x + 8
D y = 2x − 4y = 2x − 4
E y = 8
− 2

Answer 1

To determine which functions are linear, we need to analyze the given responses for their form. A function is considered linear if it can be expressed in the standard form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Here's the analysis of the provided options:

A. \(y = x - 2\)
- This is in the form \(y = mx + b\) (specifically \(m = 1\) and \(b = -2\)), so this function is linear.

B. \(y = 3x + 2\)
- This is also in the form \(y = mx + b\) (with \(m = 3\) and \(b = 2\)), so this function is linear.

C. \(y = \frac{1}{2}x + 8\)
- This is in the form \(y = mx + b\) (with \(m = \frac{1}{2}\) and \(b = 8\)), so this function is linear.

D. \(y = 2x - 4\)
- This function is in the form \(y = mx + b\) (with \(m = 2\) and \(b = -4\)), so this function is linear.

E. \(y = -2\)
- This represents a horizontal line, which can be considered linear (with slope \(m = 0\) and y-intercept \(b = -2\)).

All of the given functions A through E are linear.