Question

The line \[x+1=0\] is
(A) Parallel to X-axis
(B) Parallel to Y-axis
(C) Passing through the origin
(D) None of these

Answer 1

Hint: First of all, add -1 to the LHS and RHS in the equation of the line, \[x+1=0\] . Now, get the point having its x coordinate equal to -1 on the x-axis. Get all the possible points above and below the x-axis whose x coordinate is equal to -1. Now, join all those points and get the graph of the line \[x=-1\] . Observe the graph and conclude the answer.

Complete step by step answer:
According to the question, we have
The equation of the given line = \[x+1=0\] ………………………………………………..(1)
Now, on adding -1 to LHS and RHS in equation (1), we get
\[\Rightarrow x+1+\left( -1 \right)=0+\left( -1 \right)\]
\[\Rightarrow x=-1\]
To get the property of the line having equation \[x=-1\] , at first, we have to plot its graph.
We have to find the point \[x=-1\] on the X-axis.
We don’t have any information given for the restrictions on the y coordinates. We only have a restriction on the x coordinates that is the x coordinate of every point lying on the line must be equal to -1. Therefore, for every point lying on the line \[x=-1\] , the x coordinate should be equal to -1 whereas the y-coordinate can have any numeric value.
Now, on plotting the graph of the line \[x=-1\] , we get

In the graph, we can see that every point lying on the line has x coordinate equal to -1.
We can also observe that the line \[x=-1\] is parallel to the Y-axis.

So, the correct answer is “Option B”.

Note: Since the line \[x=-1\] is parallel to Y-axis so, option (A) can’t be true. In option (C), it is given that the line is passing through the origin but we can see that the line \[x=-1\] is not even touching the origin. So, option (C) is also not correct.