HOW TO FIND THE SLOPE FROM AN EQUATION

How to Find the Slope From an Equation ?

Here we are going to see, some example problems to find slope of the line from the given equation.

How to Find the Slope From an Equation - Questions

Question 1 :

Find the slope of the following straight lines

(i) 5y −3 = 0

Solution :

Slope (m)  =  -coefficient of x/coefficient of y

  =  0/5

  m  =  0

Hence the slope of the given line is 0.

(ii) 7 x - (3/17)  = 0

Solution :

Slope (m)  =  -coefficient of x/coefficient of y

  =  7/0

  m  = undefined

Hence the slope of the given line is undefined.

Question 2 :

Find the slope of the line which is

(i) parallel to y = 0.7x −11

Solution :

If two lines are parallel, then the slopes will be equal.

Slope of the given line :

 m = 0.7

Slope of the line parallel to the given line is 0.7

(ii)  perpendicular to the line x = −11

Solution :

x + 11  =  0

Slope of the given line  =  -1/0

  =  undefined.

Slope of the line perpendicular to the given line

  =  -1/undefined

=  0

How to Check If the Given Lines are Perpendicular

Question 3 :

Check whether the given lines are parallel or perpendicular

(i)  (x/3)+(y/4)+(1/7) = 0 and (2x/3)+(y/2)+(1/10) = 0

Solution :

Let us find the slopes of the given lines.

m = -coefficient of x/coefficient of y

Slope of the 1^st line :

  =  (-1/3)/(1/4)

m₁  =  -4/3

Slope of the 2^nd line :

  =  (-2/3)/(1/2)

m₂  =  -4/3

Since the slopes are equal, the given lines are parallel.

(ii) 5x + 23y + 14 = 0 and 23x − 5y + 9 = 0

Solution :

Let us find the slopes of the given lines.

m = -coefficient of x/coefficient of y

Slope of the 1^st line :

m₁  =  -5/23

 Slope of the 2^nd line :

  =  23/(-5)

m₂  =  -23/5

m₁ (m₂)  =  -1

Hence the given lines are perpendicular.

Question 4 :

If the straight lines 12y = −(p + 3)x +12 , 12x −7y = 16 are perpendicular then find ‘p’.

Solution :

If two lines are perpendicular, then product of their slopes = -1

Slope of the 1st line :

12y = −(p + 3)x +12

By dividing the entire equation by 12, we get

y =  [−(p + 3)/12]x + (12/12)

y =  [−(p + 3)/12]x + 1

m₁  =  -(p + 3)/12

Slope of the 2nd line :

12x −7y = 16

m = -12/(-7)

m₂  =  12/7

m₁ ⋅ m₂  =  -1

( -(p + 3)/12) (12/7)  =  -1

-(p + 3)/7  =  -1

p + 3  =  7

p  =  7 - 3

p  =  4

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

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