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.
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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
No, to be linear, both the power of x and y need to be 1. Since x is squared, the power of x is 2.
There are infinitely many solutions. One linear equation in two variables cannot be solved to give a single answer.
Since this is a linear equation with 2 variables, it is an unsolvable equation as a and b could be anything, to find an exact answer you need another equation that relates to the first one.
That looks like a linear equation (no quadratic or higher terms), so you can expect it to have a single solution. However, actually solving the equation is not difficult; do it, to confirm this.