How to read a trend and predict what happens next
TEAS 7 outline: Predict relationships among events, objects and processes
- Direct: both variables rise or fall together.
- Inverse: one variable rises while the other falls.
- Directly proportional means a straight line through the origin.
- Predict with confidence only inside the range of the data.
- For a process, follow each cause-and-effect link in order.
Key facts
- In a direct (positive) relationship, both variables increase or decrease together; in an inverse (negative) relationship, one increases as the other decreases.
- In a directly proportional relationship, doubling one variable doubles the other, and the graph is a straight line through the origin, like gas volume versus kelvin temperature at constant pressure (Charles's law).
- In an inversely proportional relationship, doubling one variable halves the other, and the graph is a curve, like gas volume versus pressure at constant temperature (Boyle's law).
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- On a graph, the independent variable usually goes on the x-axis and the dependent variable on the y-axis.
- Predictions within the range of the data (interpolation) are reasonable; predictions far outside that range (extrapolation) may not hold.
- In a cause-and-effect chain, each event triggers the next, so a change or failure in one link changes everything after it.
- In negative feedback, a sensor detects a change, a control center compares it with the normal range, and an effector reverses the change.
Quick check1 question · 2 more at the end
Which statement describes an inverse relationship between two variables?
Correct answer: B.
In an inverse relationship, one variable goes up while the other goes down. Boyle's law is the classic example: at constant temperature, increasing the pressure on a gas decreases its volume. In a direct relationship, such as Charles's law (volume and kelvin temperature at constant pressure), both variables rise together or fall together.
A Volume and temperature both increase here, so this is a direct relationship (Charles's law).
B Correct: pressure goes up while volume goes down, which is an inverse relationship (Boyle's law).
C If one variable changes while the other stays the same, there is no relationship at all, which students sometimes confuse with an inverse one.
D Volume and temperature both decrease here, so they move in the same direction, which is a direct relationship; falling values are not what makes a relationship inverse.
Full lesson
Each part starts with its main idea. Open a part when you want the details.
The short answer: To predict a relationship, find what is changed (x) and what responds (y), then describe the direction. In a direct relationship both rise or fall together; in an inverse relationship one rises as the other falls. Predict confidently only inside the range of the data, and for a process, follow each cause-and-effect link in order.
1 How do you read a trend in a table or graph?Most "predict the relationship" questions hand you a small table or graph. 1 min
Most "predict the relationship" questions hand you a small table or graph. Use the same four moves every time:
- Name the variables. What was changed on purpose (the independent variable, usually on the x-axis) and what was measured (the dependent variable, usually on the y-axis)? Read the units.
- Find the direction. As x goes up, does y go up, go down, or show no pattern?
- Find the shape. Is it a steady straight line, a curve, a rise that levels off, or a rise then a fall?
- Check the range. What are the smallest and largest x-values actually tested?
Try it on this made-up data from a student who timed how long a toy car took to roll down ramps of different heights:
| Ramp height (cm) | Time to reach bottom (s) |
|---|---|
| 10 | 2.4 |
| 20 | 1.8 |
| 30 | 1.5 |
| 40 | 1.3 |
Ramp height is the independent variable; time is the dependent variable. As height goes up, time goes down, so the relationship is inverse. The drops get smaller (0.6, then 0.3, then 0.2 s), so the graph curves and flattens rather than following a straight line.
2 What is the difference between a direct and an inverse relationship?" Directly proportional is stricter: the ratio stays constant, so the line passes through zero. 1 min
| Direct (positive) | Inverse (negative) | |
|---|---|---|
| Pattern | Both go up together, or both go down together | One goes up while the other goes down |
| Strict "proportional" version | Double x, y doubles | Double x, y halves |
| Graph of the proportional version | Straight line through the origin | Curve that bends toward the axes |
| Gas example | Charles's law: at constant pressure, volume rises with kelvin temperature | Boyle's law: at constant temperature, volume falls as pressure rises |
Two words to keep straight. A positive or direct relationship just means "same direction." Directly proportional is stricter: the ratio stays constant, so the line passes through zero. A line that rises steadily but starts at some value above zero is direct, but not directly proportional.
And remember that an inverse relationship is still a strong relationship. "No relationship" looks like scattered points or a flat line, where y doesn't change in any pattern as x changes.
3 How do you make a prediction from data?Once you know the pattern, you can estimate a value you didn't measure. 1 min
Once you know the pattern, you can estimate a value you didn't measure.
- Inside the data range (interpolation): reasonable. Say a gas sample at constant pressure fills 1.0 L at 200 K and 2.0 L at 400 K. A directly proportional pattern predicts 1.5 L at 300 K.
- Outside the data range (extrapolation): risky. The pattern might change beyond what was tested. In the ramp example, you can't assume the time keeps falling the same way for a 200 cm ramp.
On an exam, if an answer choice predicts far past the last data point and states it as certain, be suspicious.
4 How do you follow a cause-and-effect chain?Many questions describe a process and ask what happens next, or what happens if one step changes. 1 min
Many questions describe a process and ask what happens next, or what happens if one step changes. Write the process as arrows, then walk along them.
Take a normal breath in. Boyle's law says pressure and volume of a gas are inversely related, and air flows from higher to lower pressure:
Diaphragm contracts → chest cavity gets bigger → pressure in the lungs drops below the air outside → air flows in.
Now predict: if the chest cavity expanded less than usual, the pressure would drop less, and less air would flow in. You change one link and follow the arrows forward.
A useful trick is to label each arrow same (both rise or both fall) or opposite (one rises, one falls). Volume up → pressure down is an "opposite" link. Every opposite link flips the direction of the change as it passes through.
5 How do feedback loops change predictions?Your body uses negative feedback to reverse a change and return to a set point. 1 min
Your body uses negative feedback to reverse a change and return to a set point. It has three parts: a sensor that detects the change, a control center that compares it with the normal range, and an effector that acts.
If body temperature rises, sensors in the skin and brain report it. The brain's temperature-control center responds, and effectors act: skin blood vessels widen and sweat glands release more sweat, so heat is lost. Once the value is back in its normal range, the correction switches off. Blood sugar works the same way: as glucose falls back toward normal, insulin release stops, so the level doesn't keep dropping.
That gives you a prediction rule. In a negative feedback loop, the response pushes against the change. The control center can react only to what the sensor reports, and only the effector can reverse the change. So if the sensor stops detecting the change, or the effector can't act, nothing pushes back and the change keeps going.
Positive feedback does the opposite: it pushes the change further until some end point is reached, as in childbirth contractions.
Common mistakes
The traps students fall into most. Read these before you practice.
Watch out: A negative (inverse) relationship is still a relationship; no relationship means y shows no pattern as x changes.
Watch out: A straight rising line is not automatically directly proportional; it must also pass through the origin.
Watch out: An inverse relationship does not mean subtraction; when one doubles, the other halves.
Watch out: A trend inside the data does not guarantee the same trend far beyond the last data point.
Watch out: In a chain, the effect of a change depends on every link, not just the first and last events.
How to remember it
Memory hook: "Direct = same way; inverse = opposite way." For predictions: "Inside the dots, trust; outside the dots, doubt."
Self-check:
- Give one direct and one inverse example from the gas laws, and say what is held constant in each.
- A line rises steadily but crosses the y-axis at 5. Is it directly proportional? Why not?
- Draw the breathing chain with arrows and predict what happens to airflow if the diaphragm cannot contract.
Show answers
- Direct: Charles's law. At constant pressure, gas volume rises with kelvin temperature, so pressure is held constant. Inverse: Boyle's law. At constant temperature, gas volume falls as pressure rises, so temperature is held constant.
- No. Step 1: a directly proportional line must pass through the origin (0, 0). Step 2: this line crosses the y-axis at 5, not 0. So the relationship is direct (both rise together) but not directly proportional.
- Chain: diaphragm contracts → chest cavity gets bigger → pressure in the lungs drops below the air outside → air flows in. In this simple chain, if the diaphragm cannot contract, the first link fails. Follow the arrows forward: the chest cavity does not get bigger, the pressure does not drop, and air does not flow in.