Question

Find an equation of the line between (-4,2) and (1,-8)

Answer 1

The formula to calculate the equation of a line between two points is,

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`

Given

`\begin{gathered} (x_1,y_1)\rightarrow(-4,2) \\ (x_2,y_2)\rightarrow(1,-8) \end{gathered}`

Therefore,

`(y-2)/(x--4)=(-8-2)/(1--4)`

Simplify

`\begin{gathered} (y-2)/(x+4)=(-10)/(1+4) \\ (y-2)/(x+4)=-(10)/(5) \\ (y-2)/(x+4)=-2 \\ \text{Cross}-m\text{ultiply} \\ y-2=-2(x+4) \\ y=-2(x+4)+2=-2x-8+2=-2x-6 \\ \therefore y=-2x-6 \end{gathered}`

Hence, the equation of the line is

`y=-2x-6`