Question

A line passing through which of the following pairs of coordinates represents a proportional relationship?

Answer 1

D since the y-intercept would be (0,0), which means that it starts from the origin.
(haha I misread option A and B)

Answer 2

Answer:

D. (3, 6) and (4, 8)

Step-by-step explanation:

A proportion relation is defined as two variables that interact one to each other, directly. Basically its definition could be

$y=kx$

This means that the set of points must have a constant proportion $k$.

However, in this case we only have one pair of points. A specific characteristic of proportional relationship in this case is that such ratio is a whole number: ±1, ±2, ±3, ±4, ±5,... ±n.

In this case, the last pair of point fulfil this characteristic. We demonstrate that by finding the ratio, which is the slope of the linear relationship

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

Where $(x_{1} ,y_{1} )$ is the first point and $(x_{2} ,y_{2} )$ is the second point. Replacing these points, we have

$m=\frac{8-6}{4-3}=\frac{2}{1}=2$

So option D has a proportional relationship with a constant ratio of 2.