well, the cheap answer is, linear expressions have one variable and some coefficient in front of it, like 3x or 2y + 3, or (1/4)x - 15 or such, however, a LINEar expression when drawn, yields a LINE, not a curve or such, and that only happens if the variable's exponent is 1, not more than 1, if the variable's exponent is higher, then is a curve of kinds,
so such expressions like -13xy, which has the product of two variables, or 7y³ - 2 or 4x⁵ + 9, are curvy lines.