Question

How do you figure out the graph for the equation: y+5=k(x+y)+5? when k is a rational constant not equal to one.

It is appreciated if you could please explain how you find k and/or do similar questions like these.
Thank You.

Answer 1

`y` is a straight line through the origin with a slope of `k/(1-k): k in QQ: k!= 1`

Explanation:

`y+5 = k(x+y) +5`

`y cancel(+5) = k(x+y) cancel(+5)`

`y = kx+ky`

`y(1-k) = kx`

`y = (k/(1-k))x`

This is the equation of a straight line through the origin with slope of `k/(1-k)`

We are told `k in QQ: k!=1`. This leads to infinitely many lines depending on the value of `k` but not the vertical.

Thus, `y` is a straight line through the origin with a slope of `k/(1-k): k in QQ: k!= 1`