Slope and Parallel Segments

Slope and Parallel Segments

1. Find the slope of a segment.
   If a segment connects two points A(x_1, y_1) and B(x_2, y_2), use

   m = \dfrac{y_2 - y_1}{x_2 - x_1}

   This measures the rate of change: how much y changes compared with x.

2. Use parallel segments correctly.
   Parallel segments have the same slope. So if one segment is parallel to another, set their slopes equal. This is often the key step for finding an unknown coordinate or an equation.

3. Solve carefully.

   • Substitute the known points into the slope formula.
   • If you get an equation, solve it for the unknown value.
   • Simplify fractions and reduce your final answer completely.

4. Check your result.
   Make sure the slopes match exactly for parallel segments. If the slopes are written in different forms, simplify them to compare. A positive slope rises from left to right, a negative slope falls, a zero slope is horizontal, and an undefined slope is vertical.

Quick check: Recompute the slope with your final answer to verify that the segments are parallel.