Question

Passes through (3,-6) and (-1, 2)

Answer 1

Answer:

Therefore, Equation of line and the slope is

$y=-2x$

$Slope = -2$

Step-by-step explanation:

Given:  

Let,  

point A( x₁ , y₁) ≡ ( 3 ,-6)

point B( x₂ , y₂ )≡ (-1 , 2)

To Find:  

Equation of Line AB =? ( Assumption)

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,  

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

Now on substituting the slope and point A( x₁ , y₁) ≡ ( 3 , 6) and B( x₂ , y₂ )≡ (-1 , 2) we get  

$(y-(-6))=\dfrac{2--6}{-1-3}\times (x-3)\\\\y+6=\dfrac{8}{-4}(x-3)\\\\y+6=-2(x-3)\\y+6=-2x+6\\y=-2x$ .....Required Equation of line

Which is also in the form of

$y=mx$ ....Also called as Equation of line Passing through Origin.

where , m =slope

Therefore, Equation of line and the slope is

$y=-2x$

$Slope = -2$