1. **State the problem:** We need to find the equation of a line parallel to line A, which has the equation $y = mx + c$, passing through the point $P(0,5)$. 2. **Recall the formula and rules:** - The equation of a line is $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept. - Parallel lines have the same slope $m$. 3. **Analyze the given line A:** - Line A passes through the origin (since it intersects the y-axis at 0), so $c = 0$. - Its equation is $y = mx$. 4. **Find the equation of the parallel line through $P(0,5)$:** - Since the new line is parallel to line A, it has the same slope $m$. - The new line passes through $(0,5)$, so its y-intercept is $5$. 5. **Write the equation:** $$y = mx + 5$$ **Final answer:** The equation of the line parallel to $y = mx$ passing through $P(0,5)$ is $$y = mx + 5$$.