Question

How do you write the standard form of the equation given (-1,2) and slope 2?

Answer 1

`2x-1y=-4`

Explanation:

Given the point `(color(red)(hatx),color(blue)(haty))=(color(red)(-1),color(blue)2)` and a slope of `color(green)m=color(green)2`

the *slope-point form is:
`y-color(blue)(haty)=color(green)m(x-color(red)(hatx))`
`rarrcolor(white)("xxxx")y-color(blue)(2)=color(green)2(x-color(red)(""(-1)))`

We wish to convert this into standard form
`Ax+By=C` with `A,B,C in ZZ, A>=0`

Simplifying our slope-point form
`color(white)("XXX")y-2=2x+2`
Exchanging left and right sides
`color(white)("XXX")2x+2=y-2`
Subtracting `1y` from both sides:
`color(white)("XXX")2x-1y+2=-2`
Subtracting `2` from both sides:
`color(white)("XXX")2x-1y=-4`
(which is standrd form)