Question

Which equation represents a line that is parallel to the line `y=3- 2x`?

Answer 1

`y=k-2x`, where `k!=3`.

Explanation:

A line parallel to `ax+by+c=0` is of the type `ax+by+k=0`, where `k!=c`. Note this means that only constant term changes. Note that in such cases slopes of both are same i.e. `-a/b`.

Hence equation of a line parallel to `y=3-2x` is `y=k-2x`, where `k!=3`.

Note: A line pperpendicular to `ax+by+c=0` is of the type `bx-ay+k=0`. Note this means that coefficients of `x` and `y` are interchanged and relatively their sign changes. Note that in such cases slopes of both are `-a/b` and `b/a` and their product is `-1`.