Question

What is the equation of the line that goes through `(4, -1)`, and is parallel to `y=-3/2x+1`?

Answer 1

`3x+2y=10`

Explanation:

Any line parallel to `y=-3/2x+1` has the same slope i.e. `(-3/2)`

Therefore for any point `(x,y)` through `(4,-1)` parallel to this line:
`color(white)("XXX")(y-(-1))/(x-4)=-3/2`

`color(white)("XXX")2y+2=-3x+12`

`color(white)("XXX")3x+2y=10` (in "standard form")