Question

What is the equation of the line with slope `m=5/9` that passes through `(-2,-4)`?

Answer 1

`(y+4)=5/9(x+2)` [in slope-point form]
or
`5x-9y=26` [in standard form]

Explanation:

The slope-point form for a line with slope `m` through a point `(barx,bary)` is
`color(white)("XXX")(y-bary)=m(x-barx)`

Replacing the general slope and point coordinates with the given values: `m=5/9` and `(barx,bary)=(-2,-4)`
we get
`color(white)("XXX")(y-(-4))=5/9(x-(-2))`
or
`color(white)("XXX")(y+4)=5/9(x+2)`

`bar(color(white)("--------------------------------------------------------------------------))`
If you want this in "standard form"
`color(white)("XXX")Ax+By=C` with `A,B,C in ZZ; A>=0`

Multiply both sides by `9`
`color(white)("XXX")9y+36=5x+10`

Subtract `(9y+10)` from both sides
`color(white)("XXX")26 = 5x-9y`

Switch sides:
`color(white)("XXX")5x-9y=26`