there's no equals sign so it's not an equation, it's an expression. i assume you mean (a^2)/(b^8) in which case it's a non-linear expression in both a and b.
"linear in x" means the highest power of x in the expression is 1. this means there is no x^2 or x^8 etc.
2x + 4
is linear because the highest power of x is 1
2(x^3) + 4x + 7 is nonlinear because the highest power of x is 3
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If you mean y = 4x+2 then it is the linear equation of a straight line
If you mean y = 2^x, then no, it is not a linear equation. This is an exponential equation. The graph of this exponential equation would start out near zero on the left-hand side (there is a horizontal asymptote at y = 0) and would gradually increase as you move to the right: overall, it has a curved shaped. If you mean y = 2x, then yes, it is a linear equation.
-1
4x + 2y = 6
A linear equation describes a line like 2x+1=y. If you were to graph that equation, then it would give you a line. A quadratic equation is like x^2+2x+1=y. Graphing this equation would give you a U shaped graph called a parabola.