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.

1 Answer
Jun 2, 2018

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