Question

Select the functions which are proportional relationships.

[mark all correct answers]
a.
y = 4x

b.
y = x + 1

c.
y = 6x

d.
y = 2x

Answer 1

A proportional relationship can be defined as a relationship where one quantity is a constant multiple of another quantity, typically written in the form \(y = kx\), where \(k\) is a constant.

Let's analyze each of the given functions:

a. \(y = 4x\)
- This is a proportional relationship because it can be expressed as \(y = kx\) with \(k = 4\).

b. \(y = x + 1\)
- This is not a proportional relationship because it does not have the form \(y = kx\). It is a linear function with a y-intercept of 1.

c. \(y = 6x\)
- This is a proportional relationship because it can be expressed as \(y = kx\) with \(k = 6\).

d. \(y = 2x\)
- This is a proportional relationship because it can be expressed as \(y = kx\) with \(k = 2\).

In summary, the functions that are proportional relationships are:

- **a. \(y = 4x\)**
- **c. \(y = 6x\)**
- **d. \(y = 2x\)**