Question

The equation of x – axis is of the from
a. x = 0
b. y = 0
c. x + y = 0
d. x = y

Answer 1

Hint: In order to find the solution of this question, we should know about the concept of the equation of line by the slope – point formula, that is, the equation of the line passing through $\left( {{x}_{1}},{{y}_{1}} \right)$ and having the slope m is given by the formula, $\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)$. By using this concept, we will find the answer to this question.

Complete step-by-step answer:
In this question, we have been asked to find the equation of x – axis. So, to solve this question, we should have an idea about the concept of the equation of line by the slope – point formula, that is, the equation of the line passing through $\left( {{x}_{1}},{{y}_{1}} \right)$ and having the slope m is given by the formula, $\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)$. Now, we know that the point, (0,0) is the origin and it lies on the x – axis and the x – axis is a horizontal line, so the slope of x – axis will be 0. So, we can say that for ${{x}_{1}}=0,{{y}_{1}}=0$ and m = 0, we get the equation of x – axis as,
y – 0 = 0 (x - 0)
y – 0 = 0
y = 0
Hence, we can see that we obtained the equation of x – axis as y = 0. Therefore, option (b) is the correct answer.

Note: While solving this question, we can use different coordinates lying on the x – axis like (1,0), (-1,0) and so on, and then use formula, $\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)$ substitute the values and get the correct equation of x – axis, that is option (b), y = 0. The most common mistake one can make in this question is by choosing option (a), that is x = 0 as the answer, but this is actually wrong, in fact it is the equation of the y – axis.