"Linear equation" is another way to say "first-degree equation." That is, the equation involves constants and variables to the first degree only. No term contains any product or ratio of variables.
A term is first degree when the sum of all of the exponents of the variables is 1, and all exponents are positive integers. That is, the only allowed exponent of the single variable in a term is 1.
Here, the term on the left side of the equal sign has x to the first power. The term on the right side of the equal sign has y to the first power. Both are linear terms, so this is a linear equation.
