To find the equation of x-axis and of a line parallel to x-axis:
Let AB be a straight line parallel to x-axis at a distance b units from it. Then, clearly, all points on the line AB have the same ordinate b. Thus, AB can be considered as the locus of a point at a distance b from x-axis and all points on the line AB satisfy the condition y = b.
Thus, if P(x, y) is any point on AB, then y = b.
Hence, the equation of a straight line parallel to x-axis at
a distance b from it is y = b.
The equation of x-axis is y = 0, since, x-axis is a parallel to itself at a distance 0 from it.
Or
Let P (x,y) be any point on the x-axis. Then clearly, for all position of P we shall the same ordinate 0 or, y = 0.
Therefore, the equation of x-axis is y = 0.
If a straight line is parallel and below to x-axis at a distance b, then its equation is y = -b.
Solved examples to find the equation of x-axis and equation of a line parallel to x-axis:
1. Find the equation of a straight line parallel to x-axis at a distance of 10 units above the x-axis.
Solution:
We know that the equation of a straight line parallel to x-axis at a distance b from it is y = b.
Therefore, the equation of a straight line parallel to x-axis at a distance 10 units above the x-axis is y = 10.
2. Find the equation of a straight line parallel to x-axis at a distance of 7 units below the x-axis.
Solution:
We know that If a straight line is parallel and below to x-axis at a distance b, then its equation is y = -b.
Therefore, the equation of a straight line parallel to x-axis at a distance 7 units below the x-axis is y = -7.
● The Straight Line
11 and 12 Grade Math
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