FINDING THE EQUATION OF THE LINE
Finding the equation of the line :
Here we are going to see, some example problems to show finding equation of the line with the given details.
Finding the Equation of the Line - Questions
Question 1 :
Find the value of ‘a’, if the line through (–2, 3) and (8, 5) is perpendicular to y = ax +2
Solution :
Equation of the line passing through the points (-2, 3) and (8, 5).
(y - y1)/(y2 - y1) = (x - x1)/(x2 - x1)
(y - 3)/(5 - 3) = (x + 2)/(8 + 2)
(y - 3)/2 = (x + 2)/10
10(y - 3) = 2(x + 2)
10y - 30 = 2x + 4
2x + 10y - 30 - 4 = 0
2x + 10y - 34 = 0
Dividing the entire equation by 2, we get
x + 5y - 17 = 0
Question 2 :
The hill is in the form of a triangle has its foot at (19, 3) . The inclination of the hill to the ground is 45˚. Find the equation of the hill joining the foot and top.
Solution :
Equation of the hill joining the foot and top :
slope (m) = tan 45 = 1
y - y1 = m(x - x1)
y - 3 = 1(x - 19)
y - 3 = x - 19
x + y - 19 + 3 = 0
x + y - 16 = 0
Question 3 :
Find the equation of a line through the given pair of points
(i) (2, 2/3) and (-1/2, -2)
Solution :
(y - y1)/(y2 - y1) = (x - x1)/(x2 - x1)
(y - (2/3))/(-2 - (2/3)) = (x - 2)/((-1/2) - 2)
((3y - 2)/3)/(-8/3) = (x - 2)/(-5/2)
-(3y - 2)/8 = -2(x - 2)/5
5(3y - 2) = 16(x - 2)
15y - 10 = 16x - 32
16x - 15y - 32 + 10 = 0
16x - 15y - 22 = 0
(ii) (2, 3) and (-7,-1)
(y - 3)/(-1 - 3) = (x - 2)/(-7 - 2)
(y - 3)/(-4) = (x - 2)/(-9)
-9(y - 3) = -4(x - 2)
-9y + 27 = -4x + 8
4x - 9y + 27 - 8 = 0
4x - 9y + 19 = 0
After having gone through the stuff given above, we hope that the students would have understood, "Finding the Equation of the Line".
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