In this page equation of line solution13 we are going to see solution of each problem with detailed explanation of the worksheet slope of the line.

(11) Find the equation of the straight line passing through point of intersection of the lines 2 x + y – 3 =0 and 5 x + y – 6 = 0 and parallel to the line joining the points (1,2) and (2,1)

**Solution:**

The required line is passing through point of intersection of the lines 2 x + y – 3 = 0 and 5 x + y – 6 = 0 and parallel to the line joining the points (1,2) and (2,1)

First let us find the point of intersection of two lines

2 x + y – 3 = 0 ------ (1)

5 x + y – 6 = 0 ------ (2)

(1) - (2) = > 2 x + y – 3 = 0

5 x + y – 6 = 0

(-) (-) (+)

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-3 x + 3 = 0

- 3 x = -3

x = -3/(-3)

x = 1

Substitute x = 1 in the first equation

2(1) + y – 3 = 0

2 + y – 3 = 0

-1 + y = 0

y = 1

The point of intersection of two lines (1,1)

Slope of the line joining two points (1,2) and (2,1)

m = (y₂ - y₁)/(x₂ - x₁)

= (1-2)/(2-1)

m = -1

Equation of required line:

(y - y₁) = m (x - x₁)

(y – 1) = -1 (x – 1)

y - 1 = - x + 1

x + y – 1 – 1 = 0

x + y – 2 = 0

(12) Find the equation of the straight line passing through the point of intersection of the 5x – 6 y = 1 and 3x + 2y + 5 = 0 and is perpendicular to the straight line 3x – 5 y + 11 = 0.

**Solution:**

The required line is passing through point of intersection of the lines 5x – 6 y = 1 and 3x + 2y + 5 = 0 and is perpendicular to the straight line 3x – 5 y + 11 = 0.

First let us find the point of intersection of two lines

5x – 6 y = 1 ------ (1)

3x + 2y = -5 ------ (2)

(1)+(2) x 3 = > 5x – 6 y = 1

9 x + 6 y = -15

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14 x = -14

x = -14/14

x = -1

Substitute x = -1 in the first equation

5 (-1) – 6 y = 1

-5 – 6 y = 1

-6 y = 1 + 5

-6 y = 6

y = 6/(-6)

y = -1

The point of intersection of two lines (-1,-1)

Slope of the line 3x – 5 y + 11 = 0.

m = -3/(-5)

= 3/5

Equation of required line:

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

(y – (-1)) = (3/5) (x – (-1))

(y +1) = (3/5) (x +1)

5(y +1) = 3(x +1)

5 y + 5 = 3 x + 3

3 x – 5y + 3 – 5 = 0

3 x – 5 y – 2 = 0

equation of line solution13 equation of line solution13 equation of line solution13