Question

Which functions are linear?
Responses
A y = x − 2y = x − 2
B y = 3 over x + 2y = 3 x + 2
C y = 1 over 2x + 8y = 1 2 x + 8
D y = 2x − 4y = 2x − 4
E y = 8x2− 2

Answer 1

To determine which functions are linear, we need to look for functions that can be expressed in the standard linear form \(y = mx + b\), where \(m\) and \(b\) are constants.

Let's analyze each option:

A) \(y = x - 2\)
- This is in the form \(y = mx + b\) where \(m = 1\) and \(b = -2\).
- **Linear**

B) \(y = \frac{3}{x} + 2\)
- This function involves \(\frac{3}{x}\), which is not linear; it represents a hyperbola.
- **Not Linear**

C) \(y = \frac{1}{2}x + 8\)
- This is in the form \(y = mx + b\) where \(m = \frac{1}{2}\) and \(b = 8\).
- **Linear**

D) \(y = 2x - 4\)
- This is in the form \(y = mx + b\) where \(m = 2\) and \(b = -4\).
- **Linear**

E) \(y = 8x^2 - 2\)
- This function involves \(x^2\), which makes it a quadratic function, not linear.
- **Not Linear**

To sum up, the functions that are linear are:

- **A) \(y = x - 2\)**
- **C) \(y = \frac{1}{2}x + 8\)**
- **D) \(y = 2x - 4\)**