Lesson 8 of 12
Interactive lesson · prerequisites
Slope Is a Number That Describes Direction
Slope compresses the direction of a line into one number. Positive means the line rises as x increases, negative means it falls, zero means it is horizontal, and larger magnitude means steeper.
Learning goalInterpret slope as steepness with sign and magnitude.
slope = riserun = ΔyΔx
Move the idea
Try it: change one value
Move the slider
Change one parameter and watch what changes with it.
Slope is a motion rule: for each unit you move right, it tells you how much y changes.
Sign
Positive slope rises left-to-right; negative slope falls; zero slope stays level.
Magnitude
A slope of 3 is steeper than a slope of 1 because the vertical change is larger for the same horizontal run.
Why calculus needs this
A derivative asks for the slope of a curve at one point. Before that makes sense, slope itself needs to feel like a readable number rather than a memorized fraction.
Step 3 · One-question check
Did it click?
What does a slope of −2 mean?
Next: let an average slope become an instantaneous slope