Question

What is the equation of the line with slope `m= -17/25` that passes through `(47/5 32/10)`?

Answer 1

`y=-17/25*x+1199/125`

Explanation:

Such an equation has the form

`y=mx+n` where `m` is the slope and `n` the y intercept.

So we get
`y=-17/25*x+n`
plugging `x=47/5` and `y=32/10` in the equation above we can calculate `n`:

`32/10=-17/25*(47/5)+n`

doing this we get

`n=1199/125`

Answer 2

`color(indigo)(85x + 125y + 424 = 0`

Explanation:

`y - y_1 = m(x - x_1)`

`"Given : " (x_1, y_1) = (47/5, 32/10), " Slope " = m = -17/25`

`color(crimson)((y - 32/10) = (-17/25) * (x - 47/5)`

`(10y - 32 ) * 125 = -17 * 10 * (5x - 47)`

`1250y - 3750 = -850x - 7990`

`850x + 1250y = -7990 + 3750 = -4240`

`color(indigo)(85x + 125y + 424 = 0`