Question

The graph of y = 3 is a line is a line parallel to _____ axis.
A) x = 3
B) x
C) y
D) None of these

Answer 1

Hint: We will first draw the graph of the given line that is y = 3 and then, we will look at all the given axis and lines in the options and find the correct answer.

Complete step-by-step solution:
We are given the line y = 3 to find what it is parallel to. Let us draw its graph to find out the same:-

The line is red is the equation y = 3.
Now, we will go through each of the options one by one to find out the answer.
Option A:
If you notice the line x = 3 is given by:-

The line in red above is given by the equation x = 3.
We see that these both lines are perpendicular to each other.
So, option (A) is not a correct option.
Option B:
If you see in the graph given on the top, we have the x – axis actually parallel to y = 3. Hence, this is a correct option.
Option C:
We see that it is perpendicular to x = 3. It is perpendicular to the y – axis as well. Hence, this is also not a correct option.

$\therefore$ The correct option is (B).

Note: The students must note that if they find the correct answer at first option only, they must not refrain to check other options because there may be multiple correct options like if one of the options other than x – axis would have been y = a for any a other than 3, we would have still got a line parallel to y = 3, which would also be a correct answer.
The students must note that if we have an equation y = a, that means x varies and if we take the derivative of y with respect to x, we get 0 which also implies slope is parallel to x – axis and thus line is parallel to x – axis. Similarly, if we have an equation x = a, that means y varies and then if we differentiate x with respect to y, we will get 0 which also implies that slope is perpendicular to x – axis and thus line is perpendicular to x – axis.