Question

Complete the equation of the line through ( 4 , -8 ) and ( 8 , 5 )

Answer 1

Therefore the equation of the line through ( 4 , -8 ) and ( 8 , 5 ) is

13x - 4y = 84.

Explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( 4 ,-8)

point B( x₂ , y₂) ≡ (8 , 5)

To Find:

Equation of Line AB =?

Solution:

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

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

Substituting the given values in a above equation we get

`(y-(-8))=((5-(8))/(8-4))* (x-4)\\ \\(y+8)=(13)/(4)(x-4)\\\\4(y+8)=13(x-4)\\4y+32=13x-52\\13x-4y=84...............\textrm{which is the required equation of the line AB}`

Therefore the equation of the line through ( 4 , -8 ) and ( 8 , 5 ) is

13x - 4y = 84.