Can You Visualize the Line?

📌 CONCEPT: A straight line is a line that extends infinitely in two directions without any bends or curves.

📐 RULE / FORMULA: The slope of a straight line is given by the ratio of the vertical change (rise) to the horizontal change (run).

💡 WORKED EXAMPLE: If a line has a slope of 2/3, moving 3 blocks east and 2 blocks north will make you closer to the second landmark. To see this, imagine a right-angled triangle with the line as the hypotenuse. The rise is 2 units and the run is 3 units. The slope is 2/3, which is positive, indicating that the line is increasing. Moving 3 blocks east and 2 blocks north will make you closer to the second landmark.

⚠️ COMMON MISTAKE: Students often mistake the slope with the direction of the line. A positive slope does not necessarily mean the line is going up. It only indicates that the line is increasing, but the direction can be either up or down depending on the quadrant it is in.