Which equation represents a proportional relationship between the x and y values?

a) y = 2

b) y = 14x + 1

c) y = x − 4

d) y = −2x

D)

Step-by-step explanation:

A linear relationship is of the form , where, is the slope and is the y-intercept (constant).

For a proportional relationship, the value of and thus it is of the form

Let us check each option and express it in the form above.

Option A:

This can be written as . So, .

Since, b \ne 0, therefore, it is not a proportional relationship.

Option B:

Here, . So, .

Since, b \ne 0, therefore, it is not a proportional relationship.  

Option C:

Here, . So, .

Since, b \ne 0, therefore, it is not a proportional relationship.  

Option D:

This can be rewritten as

There is no y-intercept on this. So,

Since,, therefore, it is a proportional relationship.

Therefore, the correct option is D.