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 1st line :
= (-1/3)/(1/4)
m1 = -4/3
Slope of the 2nd 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 1st line :
m1 = -5/23
Slope of the 2nd 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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