Question

The line passing through (0, 2) and (−3, −1) is parallel to the line passing through (−1, 5) and (4, a) find a.​

Answer 1

Answer:-

Given:-

The lines passing through (0 , 2) ; ( - 3 , - 1) and ( - 1 , 5) ; (4 , a) are parallel to each other.

We know that,

Two parallel lines have equal slopes.

Also,

Slope of a line passing through the points (x₁ , y₁) , (x₂ , y₂) is :

Slope (m) = (y₂ - y₁) / (x₂ - x₁)

Let the slope of first line be m₁.

Here,

• x₁ = 0
• y₁ = 2
• x₂ = - 3
• y₂ = - 1

Hence,

⟹ m₁ = ( - 1 - 2) / (- 3 - 0)

⟹ m₁ = - 3/ - 3

⟹ m₁ = 1

Now,

Let the slope of second line be m₂.

Here,

• x₁ = - 1
• y₁ = 5
• x₂ = 4
• y₂ = a

⟹ m₂ = (a - 5) / (4 - ( - 1))

⟹ m₂ = (a - 5) / 5

Now,

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

⟹ 1 = (a - 5)/5

⟹ 5 = a - 5

⟹ 5 + 5 = a

⟹ a = 10

∴ The value of a is 10.

Answer 2

Given :-

The line passing through (0, 2) and (−3, −1) is parallel to the line passing through (−1, 5) and (4, a)

To Find :-

Value of a

Solution :-

We know that

$\bf Slope = \dfrac{y_2 - y_1}{x_2-x_1}$

$\sf Slope = \dfrac{-1 - 2}{-3 - 0}$

$\sf Slope = \dfrac{-3}{-3}$

$\sf Slope = \dfrac{3}{3}$

$\sf Slope = 1$

Also

$\bf Slope = \dfrac{y_2 - y_1}{x_2-x_1}$

$\sf Slope = \dfrac{a-5}{4-(-1)}$

$\sf Slope = \dfrac{a-5}{4+1}$

$\sf Slope = \dfrac{a-5}{5}$

Since, they are in parallel. Their slope must be equal

$\sf Slope_{1}=Slope_{2}$

$\sf 1 = \dfrac{a-5}{5}$

$\sf 1\times5 = a-5$

$\sf 5 = a-5$

$\sf -a = -5 - 5$

$\sf -a=-10$

$\sf a=10$