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