Question

The line \[x - 7 = 0\] is
A.Parallel to \[y\]-axis.
B.Parallel to \[x\]-axis.
C.Passing through the origin.
D.None of these.

Answer 1

Hint: We will first solve the given equation to find the value of \[x\]. We will then form a table to find the value of \[x\] with respect to \[y\]. We will then draw a graph using the table to find the nature of the line whether it is parallel to \[x\]-axis, \[y\]-axis or passing through the origin.

Complete step by step solution:
We will first solve the given equation to find the value of \[x\]. We will then form a table to find the value of \[x\] with respect to \[y\]. We will then draw a graph using the table to find the nature of the line whether it is parallel to \[x\]-axis, \[y\]-axis or passing through the origin.

\[x\]	7	7	7	7	7	7
\[y\]	\[ - 2\]	\[ - 1\]	0	1	2	3

Hence, from this table it is proved that for any value of \[y\] (both negative and positive), \[x\] will always hold the same value.
Hence, the graph of the line \[x - 7 = 0\] will be:

From this graph, we can say that it holds a constant value of \[x = 7\] and it is parallel to \[y\]-axis.

Hence, option A is the correct option.

Note: Since, the line is parallel to \[y\]-axis, clearly, it should be perpendicular to \[x\]-axis. Also, from the graph, the line makes a right angle with \[x\]-axis hence, it is perpendicular to it. The equation of a straight line parallel to \[y\]-axis at a distance ‘\[a\]’ from it is \[x = a\].
Also, the equation of a straight line parallel to \[x\]-axis at a distance ‘b’ from it is \[y = b\]. The equation of \[y\]-axis is \[x = 0\] , because \[y\]-axis is parallel to itself at a distance 0 from it. Similarly, the equation of \[x\]-axis is \[y = 0\] , because \[x\]-axis is parallel to itself at a distance 0 from it.