1. **State the problem:** We need to find the equation of a straight line that is parallel to line AB and passes through point P. 2. **Formula and rules:** - The equation of a line can be written as $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept. - Parallel lines have the same slope. 3. **Find the slope of line AB:** - Suppose the coordinates of points A and B are $A(x_1, y_1)$ and $B(x_2, y_2)$. - The slope $m$ of line AB is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 4. **Use the slope for the new line:** - Since the new line is parallel to AB, it has the same slope $m$. 5. **Find the equation of the line passing through point P:** - Let $P(x_0, y_0)$ be the point through which the new line passes. - Using point-slope form: $$y - y_0 = m(x - x_0)$$ 6. **Simplify the equation:** - Expand and rearrange to get the equation in slope-intercept form: $$y = mx - mx_0 + y_0$$ This is the equation of the line parallel to AB passing through P.