Find slope from a table
See this course’s project requirements
A linear-model comparison with tables, graphs, slope and intercept interpretations, a solved intersection and a limitation note.
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What to include
- Include input/output definitions and bounded domains.
- Provide checked tables and labeled linear graphs.
- Interpret rate and starting output with units.
- Solve an intersection and verify both outputs.
- Document a capacity-limited model and all changed-case checks.
Review and revise
Use these criteria to check your work and choose what to improve.
- Method: applies the course-specific rules to the supplied cases with visible intermediate work.
- Accuracy: results agree with the stated facts, units, boundaries and independent checks.
- Reasoning: explains why the result follows and identifies a limitation or unresolved question.
- Transfer: completes changed cases and revises the final project when a relevant assumption changes.
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The idea in everyday life
Original table: elapsed minutes 0,2,5; volume 10,18,30 L.
Slope is change in output divided by change in input. Equal input intervals help reveal a constant rate, but the method also works with unequal intervals if the denominator is used correctly.
Find slope from a table — worked practice
Slope is change in output divided by change in input. Equal input intervals help reveal a constant rate, but the method also works with unequal intervals if the denominator is used correctly.
Original table: elapsed minutes 0,2,5; volume 10,18,30 L.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Original table: elapsed minutes 0,2,5; volume 10,18,30 L. |
Copy as plain text
1. 1. Compute the first rate
Divide the volume change by the time change from minute zero to two.
You should see: (18−10)/(2−0)=4 L/min.
2. 2. Compute another rate
Use minutes two to five.
You should see: (30−18)/(5−2)=4 L/min.
3. 3. Compare rates
Decide whether the supplied points support one linear rate.
You should see: Both rates are four; the three points lie on V=10+4t.
4. 4. Explain slope
Translate the rate into a change over three minutes.
You should see: The model adds 12 L over three minutes.
What to finish
Two checked interval slopes and a constant-rate interpretation.
Watch for this
Different interval rates contradict an exact linear model.
How can I tell I understand it?
Explain a rate per unit and identify when one linear slope fails to fit a table.
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