need help with math algebra 2 is very hard and i don’t understand it

Given:
[tex]y=b^x[/tex]Find: the value of "b"
Sol:
Check for different values so.
[tex]y=b^x[/tex]At "y = 2" value of "x" is -1 then check .
[tex]\begin{gathered} y=b^x \\ \\ y=2,x=-1 \\ \\ \end{gathered}[/tex]Put the value of "x" and "y" then:
[tex]\begin{gathered} y=b^x \\ \\ 2=b^{-1} \\ \\ 2=\frac{1}{b} \\ \\ b=\frac{1}{2} \\ \\ b=0.5 \end{gathered}[/tex]So the value of "b" is 0.5