Question

18. Prove that the slope of X-axis is 0 with one example.​

Answer 1

Slope of x-axis is zero. Proved.

Step-by-step explanation:

Equation of a line with two variables x and y is as follows:

y = mx + c where m is the slope.

Now, the equation for the x-axis is that y = 0.

So the slope of x axis is 0 because the angle between the line and the x-axis is zero.

Slope = tangent of the angle between the lines.

Tan 0° = 0

Hence slope of x-axis is zero. Proved.

Answer 2

Given : Slope of x axis = 0

To find :   Show the Same with some examples

Solution:

Lets take some point on x axis

Like

(0 , 0 )  , (1 , 0)  ,  ( 2, 0)

Slope between two points  (x₁ , y₁ ) & (x₂ , y₂)

= (y₂ - y₁)/(x₂ - x₁)

Lets take (1 , 0)  ,  ( 2, 0)

Slope = ( 0 - 0)/(2 - 1)

=> Slope = 0/1

=> Slope = 0

Hence Slope of x axis  is  0

Another way

Let say Equation of  x axis is

y = mx  + c

m is the slope

c is the constant

(0,0) lies on x axis

=> 0 = 0 + c

=> c = 0

Hence Equation becomes

y  =  mx

now  (1 , 0 )  also lies on x axis

=> 0 = m(1)

=> m = 0

Hence slope of line is Zero

Also Slope of a line = Tan ( angle with x axis)

x axis angle with x axis =  0 deg

=>  Slope of  x axis = Tan (0°) = 0

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