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Inclination of a Line

TopInclination is an angle that a path of a plane makes with the axis. The minimum positive angle drawn form the positive x – axis to the line is known as Inclination of a Line.

The angle which lies between a line and x – axis is known as angle of inclination of a line. This angle lies between 0 degree to180 degrees. The line present in the horizontal part always has angle of inclination equals to zero degree. The line present in the vertical part always has angle of inclination equals to 90 degree.

The Slope of a line is given by the angle of inclination. Any number which shows the steepness of a line is known as a Slope of a line. Slope is represented by ‘m’.

The equation of line is given as:

Suppose ‘m’ is the Slope of the line and the coordinates of line is p1, q1 and p2, q2 then the equation of line is:

Slope m = tan ∅

= $\frac{q_{2} - q_{1}}{p_{2} - p_{1}}$

The slope ‘m’ for the horizontal line is zero.

The slope ‘m’ for the vertical line is undefined.

The slope of Parallel Lines is same.

Suppose for two Perpendicular Lines p1 and p2 then p1 p2 = -1;

This can also be written as:

p1 $\perp$ p2

Suppose we have the equation of line 3p + 6q – 10 = 0; and we have to calculate the inclination of the line.
Then the equation of line is:
=> 3p + 6q – 10 = 0;
This given equation of line can also be written as:
=> 3p + 6q – 10 = 0;
=> 6q = – 3p + 10;
On further solving for the variable ‘q’ we get:

=> q = – 3p + 10
6
On further solving we get:

=> $\frac{-1}{2}$ p + $\frac{10}{6}$

So the slope is m = $\frac{-1}{2}$;

And tan ∅ is – 0.5;

This is all about angle of inclination.