Question

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

Answer 1

Answer:

The equation of the line passing through the given points.

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

$y=-2x-3$

Step-by-step 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,  

$(y-y_{1})=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\times (x-x_{1})$

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

$y-(-5)=\frac{5--5}{-4-1}\times (x-1)\\ \\y+5=\frac{10}{-5}(x-1)\\ \\y+5=-2(x-1)\\y+5=-2x+2 ......Applying\ Distributive\ property\\\\y=-2x+2-5\\\\y=-2x-3....Which\ is\ required$

The equation of the line passing through the given points.

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

$y=-2x-3$