## Equation of line Solution3

In this page equation of line solution3 we are going to see solution of each problem with detailed explanation of the worksheet slope of the line.

(6) Find the equation of the straight line whose

(i) Slope is -4 and passing through (1,2)

Solution:

To find the equation of the straight line we have to use the formula of slope point form

Slope (m) = -4

x1 = 1         y 1 = 2

Equation of the line

(y - y1) = m(x - x1)

(y – 2) = -4 (x – 1)

y – 2 = -4 x + 4

4 x + y – 2 - 4 = 0

4 x + y – 6 = 0

(ii) Slope is 2/3 and passing through (5,-4)

Solution:

To find the equation of the straight line we have to use the formula of slope point form

Slope (m) = 2/3

x1 = 5         y 1 = -4

Equation of the line

(y - y1) = m(x - x1)

(y – (-4)) = (2/3) (x – 5)

(y + 4) = (2/3) ( x – 5)

3(y + 4) = 2 (x – 5)

3 y + 12 = 2 x – 10

2 x – 3 y -10 -12 = 0

2 x – 3 y – 22 = 0

(7) Find the equation of the straight line which passes through the midpoint of the line segment joining (4,2) and (3,1) whose angle of inclination is 30 degree.

Solution:

First we have to find midpoint of the line segment joining the points (4,2) and (3,1)

Midpoint = (x₁ + x₂)/2 ,(y₁ + y₂)/2

= (4 + 3)/2 , (2 + 1)/2

= 7/2 , 3/2

angle of inclination = 30°

θ = 30°

slope (m) = tan θ

= tan 30°

m = 1/√3

Equation of the line :

(y - y₁) = m (x - x₁)

[y - (3/2)] = 1/√3 [x - (7/2)]

[(2y - 3)/2)] = 1/√3 [(2x - 7)/2]

(2y - 3) = (1/√3) (2x - 7)

2√3y - 3√3 = 2x - 7

2 x - 2√3y - 7 + 3√3 = 0

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