Question

What is the equation of the line perpendicular to `y=-1/5x` that passes through `(7,4)`?

Answer 1

`5x-y=31`

Explanation:

`y=-1/5x` has a slope of `(-1/5)`
all line perpendicular to this will have a slope of `5`
(if a line has a slope of `m`, lines perpendicular to it have a slope of `(-1/m)`)

If a line has a slope `m=5` and passes through the point `(barx,bary)=(7,4)`
then we can write the equation of this line in "slope-point" form as
`color(white)("XXX")(y-bary)=m(x-barx)`

In this case
`color(white)("XXX")(y-4)=5(x-7)`

While this is a valid answer to the given question, let's convert it into standard form: `ax+by=c` with `a,b,c in ZZ; a>=0`

`color(white)("XXX")y-4=5x-35`

`color(white)("XXX")5x-y=31`