Slope Explorer Lab
Skill goal: connect rise, run, and steepness — read the slope as a simplified fraction from any two points and write the line’s equation.
Observe
Two points determine a line. Drag P1 and P2 around the grid and watch the teal rise/run triangle change shape.
Manipulate
Drag the navy points — they snap to whole-number coordinates, so every slope is an exact fraction.
Predict
Before you change it, what do you think will happen? If you drag P2 straight up while P1 stays put, will the slope get bigger, smaller, or stay the same? Make a guess, then test it.
See
Explain
Why it works: slope measures a line’s steepness as rise over run. The teal triangle shows one “step” of the line: move run units horizontally, then rise units vertically, and you land back on the line. A steeper line has a bigger slope. A vertical line has run = 0 — and division by zero is undefined, so we say its slope is undefined. A horizontal line has rise = 0, so its slope is 0 — flat, no steepness at all.
Challenge
1. Drag the points until the slope is exactly 2, then press Check.
2. Make a line with a negative slope. (Hint: it should fall as you read from left to right.) What happened to the rise?
3. Make the line vertical. What is its slope now — and why?