Question

Select the boxes of the correct answers. If a line is a direct variation passing through point C, find two additional points that lie on the same line. 6 -5 4 3 -2 1 -6 -5 -4 -3 -2 -1 0 2 3 5 --2

Answer 1

In a direct variation, y varies proportional to x, then they are represented with the general formula:

y=kx

Direct variations always pass through the origin, then, the point (0,0) always lies on the line.

Point C is located at (-4,5), then we can find the value of k from the above equation like this:

y=kx

y/x=kx/x

y/x=k

k=y/x

replacing the x and y coordinates:

k=5/-4= -5/4

Then, to know if a point lies on the line that passes through the point C, we just have to divide its y coordinate by its x coordinate and the result must be -5/4, otherwise, the point doesn't belong to the line.

From the given options, the only point that when we take its y and x coordinates and then we make y/x gives us -5/4 is the point (4,-5).

Then, points (0,0) and (4,-5) are the only points that lie on the line.