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# EQUATION OF A LINE PARALLEL TO AXES

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1. The equation of line parallel to the x-axis

Consider the figure as shown below

The equation of a line parallel to x – axis is y = y – intercept. For example a line whose y – intercept C is y = C.

2. The equation of line parallel to the y-axis

Consider the figure as shown below

The equation of a line parallel to y – axis is x = x – intercept. For example x = a is a line parallel to y – axis and perpendicular to y – axis at (a,0).

The equation of x – axis is y = 0 and the equation of y – axis is x =0.

Example

Find the equation of the line passing through (2, 3) and is parallel to x-axis and parallel to y-axis.

Solution

(a) The equation of any line parallel to x-axis is y = c.

Since the line passes through (2, 3), hence c = 3.

Therefore, the required equation is y = 3.

(b) The equation of any line parallel to y-axis is x = a.

Since the line passes through (2, 3), hence a = 2.

Therefore, the required equation is x = 2.

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