Question

Write an equation of the line passing through the given points.

(1,-5) and (-4,5)

y=?

can some help? ​

Answer 1

The equation of the line passing through the given points.

(1,-5) and (-4,5) is

`y=-2x-3`

Explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( 1 ,-5)

point B( x₂ , y₂ )≡ (-4 , 5)

To Find:

Equation of Line AB =?

Solution:

Equation of a line passing through a points A( x₁ , y₁) and point B( x₂ , y₂ ) is given by the formula Two -Point Form,

`(y-y_(1))=(y_(2)-y_(1) )/(x_(2)-x_(1) )* (x-x_(1))`

Now on substituting the slope and point A( x₁ , y₁) ≡ ( 1 ,-5) and B( x₂ , y₂ )≡ (-4 , 5) we get

`y-(-5)=(5--5)/(-4-1)* (x-1)\\ \\y+5=(10)/(-5)(x-1)\\ \\y+5=-2(x-1)\\y+5=-2x+2 ......Applying\ Distributive\ property\\\\y=-2x+2-5\\\\y=-2x-3....Which\ is\ required`

The equation of the line passing through the given points.

(1,-5) and (-4,5) is

`y=-2x-3`