Question

Please help? Medal + Fan! <3

Compare a direct variation to a linear relationship. How are they similar? How are they different?

Answer 1

Okay, so linear equation is any line, like \(\large\color{black}{ y=mx+b }\).
Direct variation, is defined by \(\large\color{black}{ y=kx }\) (where "k" is constant)

So linear relationship is not necessarily a direct variation -- usually not, (unless b=0).

Answer 2

You can see that in a linear relationship
\(\large\color{black}{ y=mx+b }\) where \(\large\color{black}{ b }\) is real.

And direct variation, is also,
\(\large\color{black}{ y=mx+b }\) but on a condition that \(\large\color{black}{ b=0 }\).

Answer 3

@KamiBug

Answer 4

basically.
Linear relationship is any line
Direct variation, is a line that (must be/ is) going through the origin, though (0,0)

Answer 5

@SolomonZelman Thank you so so much!

Answer 6

Yes, just a couple examples of direct variations.
https://www.desmos.com/calculator/addhotulo9
(keep in mind that a direct variation is always a linear relationship to, which is not true the other way. Linear relationship is not necessarily a direct variation.)