1. **State the problem:** We need to find the equation of a line parallel to line A that passes through point P. 2. **Identify the slope of line A:** Line A passes through points (0,0) and (1,1). 3. **Calculate the slope $m$ of line A:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 0}{1 - 0} = 1$$ 4. **Parallel lines have the same slope:** So the line we want also has slope $m = 1$. 5. **Use the point-slope form of a line equation:** $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1)$ is point P $(0,2)$. 6. **Substitute values:** $$y - 2 = 1(x - 0)$$ 7. **Simplify:** $$y - 2 = x$$ 8. **Rewrite in slope-intercept form $y = mx + c$:** $$y = x + 2$$ **Final answer:** The equation of the line parallel to line A passing through point P is $$y = x + 2$$