Is the graph a linear function, non linear function, or relation

a LINEar function has well, the graph of a straight line, so this isn't that.

is it a relation? well, yes, because the y-value correlates with the x-value, so one depends or relates to the other.

is it a non-linear function?  well, a function has to pass the vertical line test, meaning if we draw vertical lines they must touch the graph only once on their way down and in this case it seems they do, so it is non-linear clearly, and it's also a function.

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0