Question

Which of the following represent a line parallel to x-axis?
A. $x + y = 3$
B. $2x + 3 = 7$
C. $2 - y - 3 = y + 1$
D. $x + 3 = 0$

Answer 1

Hint : In order to solve this question let me tell you that for the line which is parallel to x-axis it is must that the slope of the line should be equal to zero which means if the line is parallel to x-axis there will be only the equation where there will be not x term present and the equation is only in form of independent term.

Complete step by step solution:
For solving this question we will first know that since the slope is equation is equal to zero so the equation of line will be:
$y = mx + c$
Since the value of m=0 so the equation will be:
$y = 0x + c$
Now on further solving:
$y = c$ ………(1)
Now from this it is clear that the equation will be in the form of this equation and there will be no x term.
Now we will check one by one which of the above equations are in terms of equation (1)

A. $x + y = 3$
This is clearly not in terms of equation because here the term of x is also present.

B. $2x + 3 = 7$
Here we can see that this equation has not the present the y term so but here only present the x term so this line will be parallel to y-axis.

C. $2 - y - 3 = y + 1$
On further solving this equation we will get the new transformed equation that is:
$y = - 1$
This is the equation which is present in terms of y=c, where c is any constant.

D. $x + 3 = 0$
As in option B this will be also parallel to the y-axis because is purely in terms of x.
So the correct option will be C.
So, the correct answer is “Option C”.

Note : While solving these types of problems we should keep in mind that we can‘t say anything just by looking at the equations directly so we should first solve it into the simplest form then we will check it in forms of the required equation. And the equation in pure terms of y will be parallel to x-axis similarly the equation purely in terms of x will be parallel to y axis.