Question

How do you write an equation in standard form given a line that passes through (22,12) with slope 5/6?

Answer 1

A line passing through `(22, 12)` with slope `5/6` can be expressed using the point slope form as:
`color(white)("XXXX")` `y-12 = 5/6(x-22)`

The standard form for a line is
`color(white)("XXXX")` `Ax+By=C` where `A>=0, A epsilon ZZ`

So a bit of manipulation of the point slope form is required
`color(white)("XXXX")` `6(y-12) = 5(x-22)`

`color(white)("XXXX")` `6y-72 = 5x -110`

`color(white)("XXXX")` `-5x +6y = - 38`

`color(white)("XXXX")` `5x -6y = 38` `color(white)("XXXX")`(standard form)