Question

What is the equation of the line determined by the points (3,0) and (0,2)?

Answer 1

`"answer : "-2x-3y=-6`

Explanation:

`"let P(x,y) be a point on the line AB.This point splits the line"` `"segment AB into two part. The line segments PB and PA "`
`"have the same slope."`

`tan alpha=((2-y))/((x-0))" , "tan beta=((y-0))/((3-x))`

`"Since "alpha=beta " ,we can write as " tan alpha=tan beta.`

`((2-y))/((x-0))=((y-0))/((3-x))`

`(2-y)/x=y/(3-x)`

`x y=(2-y)(3-x)`

`x y=6-2x-3y+x y`

`cancel(x y)=6-2x-3y+cancel(x y)`

`-2x-3y=-6`