The figure above shows the graph of a function f, defined by f(x) = |2

We are looking for intersection in the first quadrant because all lines in the given five options have positive slope. A line with positive slope definitely passes through the first and third quadrant. So we are ignoring second quadrant for the time being.

If you understand how lines are drawn on xy axis, you can do this question in 10 seconds.

The graph of f(x) is shown. The line in first quadrant has slope 2.

Let's plot all lines on the xy axis.




We know y = x is a line making 45 degree angle with y axis and passing through the centre. Point at it in the given figure.
y = x - 2 will be two steps below it passing through (0, -2)
y = x + 3 will be two steps above it passing through (0, 3)
They both have slope 1 which is less than the slope of f(x). They will not intersect f(x).

Now hold on to y = 2x, a line passing through (0, 0) but with a steeper slope. The slope is the same as that of f(x) so it is parallel to f(x).
Both y = 2x - 2 and y = 2x + 3 (blue lines) will have slopes parallel to f(x) and will not intersect it.

The only remaining line is 3x - 2 (green line) which is steeper than f(x) and will intersect it.