Is y=x+1/5 a linear equation?

Question

Is y=x+1/5 a linear equation?

Answer 1

yes

highest exponent of the variables x and y is 1, an implicit 1,

y= x + 1/5 is the same as

y^1 = x^1 + (1/5)x^0 (an implicit x^0 or y^0 = the constant term)

to be non-linear means the exponent is not 1.

"linear" comes from "line(r) a straight line is the graph of the equation y=x + 1/5

It's a straight line with slope 1 and y intercept = 1/5

BUT "frequently" the term "linear equation" refers to an equation with juse one variable, with an exponent of 1.

such as x + 1/5 = 0

then there is a unique solution: x =-15

with more than one variable, there is an infinite number of solutions, graphically it's a line where every point on the line is a possible solution to the linear equation.

y = x + 1/5 has an infinite number of solutions, such as

x y

1 6/5

2 11/5

0 1/5

-1 -4/5

-2 -9/5

-3 -14/5

or other larger or smaller x integers or any real number, integer, rational or irrational, for x and y