(05.01) Which statement best explains if the graph correctly represents the proportional relationship y = −2x?
A coordinate plane is shown. Points are graphed at 2 comma 4 and negative 1 comma 2. The points are joined by a line.

No, the points shown would not be part of y = −2x
No, proportions cannot be represented on a graph
Yes, all proportions can be shown on a graph of this line
Yes, the points shown on the line would be part of y = −2x

You missed adding the graph. After a little research, I am potentially able to find the graph. So, I am attaching the picture.

YES, the points shown on the line would be part of y = −2x.

Hence, option D is true.

Step-by-step explanation:

We know that when y varies directly with x, we get the equations such as

y ∝ x

y = kx

where k is the constant of variation.

Given the proportional relationship

y = −2x

so the value of k = -2

From the attached graph, it is clear that the points are (-2, 4) and (-1, 2)

substituting x = -2 and y = 4 in the equation

4 = -2(-2)

4 = 4

TRUE!

L.H.S = R.H.S

Hence, the point (-2, 4) is on the line y = −2x

In other words, the points (2, 4)

k = y/x

k = 4/-2

k = -2

Hence, the values of k correctly matches with the k value (k=2) in the  equation y = -2x.

substituting x = -1 and y = 2 in the equation

2 = -2(-1)

2 = 2

TRUE!

L.H.S = R.H.S

Hence, the point (-1, 2) is on the line y = −2x

In other words, the points (-1, 2)

k = y/x

k = 2/-1

k = -2

Hence, the values of k correctly matches with the k value (k=2) in the  equation y = -2x.

Therefore, we conclude that YES, the points shown on the line would be part of y = −2x.

Hence, option D is true.