## Equation of line Solution13

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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

(-) (-)
(+)

----------------

-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

-----------------

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