Slope: Intuitive Introduction

Below is a ramp represented by a right triangle. Right now, the green (vertical) leg of the triangle has a length of 5, and the red (horizontal) leg has a length of 9. What is the displayed value of the slope of the ramp?

Now drag only one of the white points so that the length of the green (vertical) leg is 4. What is the displayed slope now, and is the ramp steeper or less steep than when the slope was ?

Now drag whichever of the white points you need to so that the length of the green (vertical) leg is 4 and the length of the red (horizontal) leg is 3. What is the displayed slope of the ramp now, and is it more or less steep than when it was ?

If the displayed slope is then which statement is FALSE? (If you need to use the applet to decide, feel free!)

Move the points so that the green (vertical) leg is 4 and the red (horizontal) leg is 8. Note the displayed slope. Repeat with respective leg lengths 3 and 6, then 2 and 4, then 1 and 2. What is true?

Now move the white points whichever way you need to so that the displayed slope of the ramp is negative. What effect does this have on the ramp?

Write a few sentences about what you've noticed about slope. Here are some guiding questions (but you don't have to use these to write your reflections):

• How is steepness measured?
• What caused the ramp to be more steep, or less steep?
• What does negative slope mean?
• If two ramps have the exact same steepness, what must be true about their slopes?