Which is a counterexample for the conditional statement shown?

if two distinct points are graphed on a coordinate plane, then the line connecting the points can be represented with a function.

the points have the same x-coordinate value.
the points have the same y-coordinate value.
the points follow the rule (x, y) (–x, –y).
the points follow the rule (x, y) (–y, –x).

First Option

The points have the same x-coordinate value.

Step-by-step explanation:

By definition, a relation is considered a function if and only if for each input value x there exists only one output value y.

So, the only way that the line that connects two points in the coordinate plane is not a function, is that these two points have the same coordinate for x.

For example, suppose you have the points (2, 5) and (2, 8) and draw a line that connects these two points.

The line will be parallel to the y axis.

Note that the value of x is the same x = 2. But when x = 2 then y = 5 and y = 8.

There are two output values (y = 8, y = 5) for the same input value x = 2.

In fact all the vertical lines parallel to the y-axis have infinite output values "y" for a single input value x. Therefore, they can not be defined as a function.

Then the correct option is:

The points have the same x-coordinate value.