HOW TO FIND THE SLOPE WITH ANGLE OF INCLINATION

Let θ be the angle of inclination and m be the slope of the line. 

Then, the relationship between the angle of inclination and slope of the line is given by 

m  =  tanθ

Example 1 :

Find the slope of the line whose angle of inclination is 30°.

Solution :

The relationship between the angle of inclination θ and slope of the line m is given by 

m  =  tanθ

Given : θ  =  30°.

Then, 

m  =  tan 30°

m  =  1/√3

So, the slope of the line is 1/√3. 

Example 2 :

Find the slope of the straight line whose angle of inclination is 60°.

Solution :

The relationship between the angle of inclination θ and slope of the line m is given by 

m  =  tanθ

Given : θ  =  60°.

Then, 

m  =  tan 60°

m  =  √3

So, the slope of the line is √3. 

Example 3 :

Find the slope of the straight line whose angle of inclination is 90°.

Solution :

The relationship between the angle of inclination θ and slope of the line m is given by 

m  =  tanθ

Given : θ  =  90°.

Then, 

m  =  tan 90°

m  =  undefined

So, the slope of the line is undefined. 

Example 4 :

Find the slope of the straight line whose angle of inclination is 45°.

Solution :

The relationship between the angle of inclination θ and slope of the line m is given by 

m  =  tanθ

Given : θ  =  45°.

Then, 

m  =  tan 45°

m  =  1

So, the slope of the line is 1. 

Example 5 :

The side AB of a square ABCD is parallel to x-axis . Find the

(i) slope of AB

(ii) slope of BC

(iii) slope of the diagonal AC

Solution :

(i)  Slope of AB :

Because the side AB is parallel to x-axis, angle formed by the side AB with x-axis is zero.

Then, 

m  =  tan 0°

m  =  0

So, the slope of the side AB is 0.

(ii)  Slope of BC :

If the side AB is parallel to x-axis, then the side BC will be perpendicular to x-axis.

So, it forms the angle 90° with axis.

Then, 

m  =  tan 90°

m  =  undefined

So, the slope of the side BC is undefined.

(ii)  Slope of the diagonal AC :

Because AC is diagonal, the angle of inclination of the diagonal AC with x-axis is 45°.

Then, 

m  =  tan 45°

m  =  1

So, the slope of the diagonal AC is 1.

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