Question

How do you write an equation of the line in standard form that is Parallel to 5y-4x=15 and through (10,6)?

Answer 1

`4x-5y=10`

Explanation:

`5y-4x=15` has a slope of `4/5`

The slope-point form of a linear equation is
`color(white)("XXX")(y-haty) = m(x-hatx)`
`color(white)("XXXXXXX")`where `m` is the slope and `(hatx,haty)` is a point

For this example we have
`color(white)("XXX")(y-6) = 4/5(x-10)`

Simplifying:
`color(white)("XXX")y=4/5x-8+6`

`color(white)("XXX")5y=4x-10`

Standard form is
`color(white)("XXX")Ax+By=C` with `A, B, C in ZZ, A>=0`

Converting to standard form:
`color(white)("XXX")4x-5y=10`