In this page equation of line solution11 we are going to see solution of each problem with detailed explanation of the worksheet slope of the line.

(4) If the straight lines y/2 = x – p and ax + 5 = 3 y are parallel, then find a

**Solution:**

y/2 = x – p

y = 2(x-p)

y = 2 x – 2 p

3 y = ax + 5

y = ax/3 + 5/3

m1 = 2

m2 = a/3

If two lines are parallel then

Slope of the first line (m1) = Slope of the second line (m2)

2 = a/3

a = 6

(5) Find the value of a if the straight lines 5 x – 2 y – 9 = 0 and ay + 2 x – 11 = 0 are perpendicular to each other.

**Solution:**

If two lines are perpendicular then

Slope of the first line (m1) x Slope of the second line (m2) = -1

m1 = -5/(-2)

= 5/2

m2 = -a/2

(5/2) x (-a/2) = -1

-5a/4 = -1

-5a = -4

a=-4/(-5)

a =4/5

(6) Find the value of p for which the straight lines 8 px + (2-3p) y + 1 = 0 and px + 8 y – 7 =0 are perpendicular to each other.

**Solution:**

Slope of the line 8 px + (2-3p) y + 1 = 0

m1 = -8p/(2-3p)

Slope of the line px + 8 y – 7 =0

m2 = -p/8

If two lines are perpendicular m1 x m2 = -1

-8p/(2-3p) x (-p/8) = -1

p²/(2-3p) = -1

p² = -1(2-3p)

p² = -2 + 3p

p²- 3p + 2 = 0

(p - 1) (p - 2) = 0

p – 1 = 0 p – 2 = 0

p = 1 p = 2

(7) If the straight line passing through the points (h,3) and (4,1) intersects the line 7 x – 9 y – 19 = 0 t a right angle, find the value of h.

**Solution:**

The line is passing through the points (h,3) and (4,1) and it is intersecting the line 7 x -9 y – 19 = 0. So we can say that these two lines are perpendicular.

If two lines are perpendicular then

slope of the first line (m₁) x slope of the second line (m₂) = -1

m₁ = (y₂ - y₁)/(x₂ - x₁)

= (1-3)/(4-h)

m₁ = -2/(4-h)

m₂ = -7/(-9)

m₂ = 7/9

[-2/(4-h)] x [7/9] = -1

[2/(4-h)] x [7/9] = 1

14/9(4-h) = 1

14 = 36 – 9 h

9 h = 36 – 14

9 h = 22

h = 22/9

equation of line solution11 equation of line solution11