Question

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

Answer 1

Answer:

D) $y=-2x$

Step-by-step explanation:

A linear relationship is of the form $y=mx+b$, where, $m$ is the slope and $b$ is the y-intercept (constant).

For a proportional relationship, the value of $b=0$ and thus it is of the form $y=mx$

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

Option A:

$y=2$

This can be written as $y=0x+2$. So, $b\ne 0$.

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

Option B:

$y=14x+1$

Here, $b=1$. So, $b\ne 0$.

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

Option C:

$y=x-4$

Here, $b=-4$. So, $b\ne 0$.

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

Option D:

$y=-2x$

This can be rewritten as $y=-2x+0$

There is no y-intercept on this. So, $b=0$

Since,$b = 0$, therefore, it is a proportional relationship.

Therefore, the correct option is D.

Answer 2

Answer:

The Anwser is D

Step-by-step explanation: