Question

A direct variation always goes through the origin of the coordinate plane. a. True b. False

Answer 1

True 

A direct variation always goes through the origin of the coordinate plane is a correct statement.

Answer 2

Answer :  The given statement is TRUE.

Step-by-step explanation:  The given statement is

"A direct variation always goes through the origin of the coordinate plane."

We are to check whether the above statement is true or false.

In the two dimensional coordinate, let the Y-coordinate (y) varies directly as the X-coordinate (x).

Then, we can write

$y\propto x\\\\\Rightarrow y=kx,~~\textup{where 'k' is the constant of proportionality}.$  

We see that, for any real number 'k',

the equation y = kx is the equation of a straight line passing through the origin, because when x = 0, then y = 0.

So, (0, 0) is always a point on the line y = kx. That is, the line will always pass through the origin.

Thus, a direct variation always goes through the origin of the coordinate plane. The statement is TRUE.

If we take k = 2, then the equation becomes y = 2x. The graph of the line is shown in the attached figure. We see that the line passes through the origin.