Question

How do you write the standard form of the equation given (3,5) and slope 5/3?

Answer 1

`5x-3y=0`

Explanation:

Start with the slope-point form: `(y-color(blue)(y_1))=color(green)m(x-color(red)(x_1))`
with the point `(color(red)3,color(blue)5)` and slope `color(green)(5/3)` to get:
`color(white)("XXX")y-color(blue)5=color(green)(5/3)(x-color(red)3)`

Our target form is the standard form: `Ax+By=C`

Multiplying both sides of our slope-point form by `3`
and expanding the left side:
`color(white)("XXX")3ycancel(-15)=5xcancel(-15)`

Re-arrange into standard form:
`color(white)("XXX")5x-3y=0`