1. **State the problem:** We need to find the equation of a line parallel to line A that passes through point P(0, 3). 2. **Find the slope of line A:** The slope $m$ is given by the formula $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1) = (-6, -5)$ and $(x_2, y_2) = (6, 3)$. 3. **Calculate the slope:** $$m = \frac{3 - (-5)}{6 - (-6)} = \frac{3 + 5}{6 + 6} = \frac{8}{12}$$ 4. **Simplify the slope:** $$m = \frac{\cancel{8}}{\cancel{12}} = \frac{2}{3}$$ 5. **Use the slope-point form to find the equation of the parallel line:** The slope of the parallel line is the same, $m = \frac{2}{3}$. The point is $P(0, 3)$. The equation is $$y = mx + c$$ Substitute $x=0$, $y=3$, and $m=\frac{2}{3}$: $$3 = \frac{2}{3} \times 0 + c$$ 6. **Solve for $c$:** $$c = 3$$ 7. **Write the final equation:** $$y = \frac{2}{3}x + 3$$ This is the equation of the line parallel to line A passing through point P.