Grade 9 · Linear functions
Ticket model: Interpret signed slope and intercept
Ticket model investigation: interpret signed slope and intercept. Change the quantities, follow the motion, and explain the result using the displayed mathematical relationship.
Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.
Watch the relationship
PausedHD animation studio
From experiment to screen.
Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.
Understand what you are seeing
The idea behind the motion.
In y=mx+b, the slope describes output change per input unit and the intercept gives the output at zero. Changing b translates a graph while leaving its rate unchanged. A negative slope means output decreases as input increases; zero slope gives a constant function. This investigation begins with slope m = -1; intercept b = -3. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.
A relationship to keep
y = mx + b; Δy/Δx = m
Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.
- STEP 1
Represent the given quantities
Find the intercept on the vertical axis before using the slope to predict another point.
- STEP 2
Follow the changing model
Playback moves an input from −5 to 5. The point's output is recomputed from the exact linear rule.
- STEP 3
Check and explain the relationship
Compare two points and divide their output difference by their input difference to check the slope.
Your turn to explain
Make a prediction. Test your reasoning.
Ticket model: For y = -1x + (-3), find y when x = 3.
Use the values specified in the question. Reset restores the initial values for this investigation.
Compare your explanation
y = -6; multiply three by the slope and then add the intercept.
Work through a full lesson
Connect the animation to a worked example and practice questions.