Question

What is the equation of the line perpendicular to `y=-2x` that passes through `(4,-1)`?

Answer 1

`" "color(green)(y=1/2x-3)`

Explanation:

Suppose the slope (gradient) of the original equation was m. Then we would have: `y=mx`

The line perpendicular would have the gradient of `(-1)xx1/m`

So for your equation `m=(-2)`

That means that the line perpendicular will have the gradient of

`(-1)xx 1/(-2)" "=" "+1/2`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So the new equation is: `y=1/2x`

The thing is that it should be `color(brown)(y=1/2x+c)`

where c is a constant value
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To find the value of c")`

We are given that `color(blue)((x,y)->(4,-1))`
So by substitution we have:

`" "color(brown)(color(blue)(-1) =1/2(color(blue)(4))+c`

`" "-1=2+c`

`" "c=-3` giving

`" "color(green)(y=1/2x-3)`