In each of the following statements fill in the blanks with always sometimes or never.

1. If the ordered pair (x,y) is not a solution to an equation in two variables, then the point (x,y)is on the graph ______________.

2. The graph of a horizontal line ______________ passes through the origin.

Here are my answers.
1. Never
2. Never

first correct. Second: what if the horizontal line is the x axis?

Can you give me an example equation that describes the relationships between x and y. I think that would help me understand the two statements better. Thanks

Certainly! Let's consider the equation y = 2x as an example equation that relates x and y.

1. If the ordered pair (x, y) is not a solution to an equation in two variables, then the point (x, y) is on the graph sometimes.
Explanation: The graph of an equation represents all the points (x, y) that satisfy the equation. If an ordered pair (x, y) is not a solution to an equation, it means that substituting x and y into the equation does not make it true. Therefore, this point does not lie on the graph of that equation. However, it is possible for the point (x, y) to lie on the graph of another equation.

2. The graph of a horizontal line sometimes passes through the origin.
Explanation: In general, a horizontal line can have an equation of the form y = k, where k is a constant. If k = 0, then the equation becomes y = 0, which represents the x-axis. In this case, the horizontal line coincides with the x-axis and passes through the origin (0, 0). However, if k ≠ 0, then the line will not pass through the origin.

Therefore, the correct answers to the statements are:

1. If the ordered pair (x, y) is not a solution to an equation in two variables, then the point (x, y) is on the graph sometimes.
2. The graph of a horizontal line sometimes passes through the origin.