HOW TO FIND SLOPE OF THE LINE

How to Find Slope of the Line ?

Here we are going to see, finding area of triangle and quadrilateral with vertices.

Methods to Find Slope of the Line

(1)  If θ is the angle of inclination of a non-vertical straight line, then tan θ is called the slope or gradient of the line and is denoted by m.

m  =  tan θ

(2)  To find the slope of a straight line when two points are given

m = (y2 - y1)/(x2 - x1)

(3)  To find the slope of a straight line when equation of the line is given 

m = -coefficient of x/coefficient of y

(4)  If two lines are parallel, then its slopes will be equal.

m1  =  m2

(5)  If two lines are perpendicular, then the product of their slopes

m1 x  m=  -1

How to Find Slope of the Line - Questions

Question 1 :

What is the slope of a line whose inclination with positive direction of x -axis is

(i) 90° (ii) 0

Solution :

(i)  θ  =   90°

m = tan θ

m = tan 90°

  m  =  undefined

(i)  θ  =   0°

m = tan θ

m = tan 

  m  =  0

Question 2 :

What is the inclination of a line whose slope is (i) 0 (ii) 1

Solution :

(i)  0

m = 0

tan θ  =  0

Hence the required angle of inclination is 0.

(ii) 1

m = 1

tan θ  =  1

Hence the required angle of inclination is 45°.

Question 3 :

Find the slope of a line joining the points

(i) (5, 5) with the origin 

Solution :

m = (y2 - y1)/(x2 - x1)

x1  =  5, x2  =  0, y1  =  5 and y2  =  0

  m  =  (0 - 5)/(0 - 5)

  m  = -5/(-5)

  m  =  1

(ii) (sin θ, -cos θ) and (-sin θ , cos θ)

Solution :

x1  =  sin θ, x2  = -sin θ, y1  =  -cos θ and y2  =  cos θ

  m  =  (cos θ - (-cos θ))/(-sin θ - sin θ)

  m  =  (cos θ + cos θ)/(-sin θ - sin θ)

  m  =  (2cos θ)/(-2sin θ)

  m  =  -cos θ/sin θ

   m  = cot θ

Question 4 :

What is the slope of a line perpendicular to the line joining A(5,1) and P where P is the mid-point of the segment joining (4,2) and (-6, 4) .

Solution :

P is the mid-point of the segment joining (4,2) and (-6, 4) 

First, let us find the point P.

 midpoint  =  (x1 + x2)/2, (y1 + y2)/2

  =  (4+(-6))/2, (2 + 4)/2

  =  -2/2, 6/2

  =  P(-1, 3)

Now, we have to find the slope of the line which is perpendicular to the line joining the points A(5, 1) and P(-1, 3).

Slope of AP x slope of the required line  =  -1

Slope of AP  =   (y2 - y1)/(x2 - x1)

Slope of AP  =   (3 - 1)/(-1 - 5)

  =  2/(-6)

  =  -1/3

Slope of required line  =  -1/(-1/3)

  =  3

After having gone through the stuff given above, we hope that the students would have understood, "How to Find Slope of the Line". 

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