\(y=mx+b\)

The lines are parallel when their m (slope) is the same.

\(\displaystyle{m}=\frac{{4}}{{5}}\)

Find b by substituting \(\displaystyle{m}=\frac{4}{{5}}\) and \((1,2)\):

\(\displaystyle{2}=\frac{{4}}{{5}}{\left({1}\right)}+{b}\)

\(\displaystyle{2}=\frac{{4}}{{5}}+{b}\)

\(\displaystyle{b}=\frac{{6}}{{5}}\)

Thus, the expression is:

\(\displaystyle{y}=\frac{{4}}{{5}}{x}+\frac{{6}}{{5}}\)