Question

Which line represents the direct variation equation y = 1/2 x?

Answer 1

again, you need to remember that EVERY straight line has the equation

                 y = (slope) x + (y-intercept) .

Right away, you know that this line goes through the origin ...
the equation doesn't show any y-intercept.  The y-intercept is zero,
meaning that the line crosses the y-axis at the place where y=0.
That's the origin ... the place where the x- and y-axes cross.

Look at the graph they gave you. ... At first it looks like an ugly mess.
But look closer.  There are only two lines there that go through the origin,
so one of those is the answer to the question.

Now let's talk about the slope of a line.
  
-- If the slope of a line is positive, that means it rises as it goes.
   If you walk the graph from left to right, you're climbing.

-- If the slope of a line is negative, that means it falls as it goes.
   If you walk the graph from left to right, you're going down-hill.

The equation they gave you is  [ y = 1/2 x ].
The slope is  1/2 .  That's positive.
The line on the graph slopes up.  To walk it, you have to climb.

In the picture, that can only be line 'c' .