1. Problem: Draw a line parallel to a given line so you can see what “parallel” means. 2. Key idea (parallel lines): Parallel lines have the same direction, so their slopes are equal. 3. If the given line is $y=mx+b$, then the line parallel to it has the same slope $m$ and a different intercept $b_1$. 4. General formula for a parallel line: $$y=mx+b_1$$ 5. Rule for choosing the intercept $b_1$: - Pick a point $P(x_0,y_0)$ that the new parallel line should pass through. - Substitute $x_0,y_0$ into $y=mx+b_1$ to solve for $b_1$. 6. Solve for $b_1$: $$y_0=mx_0+b_1$$ $$b_1=y_0-mx_0$$ 7. Final answer (equation of the parallel line): $$y=mx+(y_0-mx_0)$$ 8. What to draw on the diagram: - Mark the given line. - Pick the point $P$ off (or on) the given line. - Draw the new line through $P$ with the same direction as the given line. - That new line is the one parallel to the given line.