Step 1 :Find the slope of the given line $y=x+7$, which is 1.
Step 2 :Use the point-slope form of a line equation $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is the point the line passes through.
Step 3 :Substitute the slope $m=1$ and the point $(2,4)$ into the point-slope form to get the equation of the parallel line.
Step 4 :Simplify the equation to get the final answer: $y = x + 2$.
Step 5 :Final Answer: \(\boxed{y = x + 2}\)