Question

The point on the graph below is an element of a direct variation. Identify two other points from the choices given that are also elements of this direct variation.

-4, -2
0, -1
0, 0
4, 2
2, 4
-3, ,8

Answer 1

Answer: (0, 0) and (2, 4)

Explanation:

Direct variation can be written as y = kx, where (x, y) is a coordinate point and k is a constant.

These graphs go through the origin, (0, 0), so we know that is another point.

We can find our second point by viewing the point on the graph. This value is at (-2, -4). Using the slope formula (change in y over change in x), gives us a slope of 2, which is equal to our k value. See this work below. Using this value of k, we can find any other point in this direct variation. Submitting 2 into y = 2x gives us y = (2)(2) = 4, which is another answer option. This gives us our second point, (2, 4).

`\displaystyle (y_(2) -y_(1) )/(x_(2) -x_(1) ) =(0-4)/(0-2)=(-4)/(-2) =2`

Now we have our two coordinate points, (0, 0) and (2, 4).