Graph a linear relationship
See this course’s project requirements
A linear-model comparison with tables, graphs, slope and intercept interpretations, a solved intersection and a limitation note.
Keep your working files in your own notebook or software. Save a private description, checklist, and work link in My Proof.
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.
Want more background?
The idea in everyday life
Original case: V=4+3t for 0≤t≤4; liters versus elapsed minutes.
A graph connects a relationship to positions on labeled axes. Use input on the horizontal axis, output vertically, and evenly spaced numerical scales. A line segment preserves a bounded continuous domain; discrete allowed inputs may require points rather than every intervening value.
Graph a linear relationship — worked practice
A graph connects a relationship to positions on labeled axes. Use input on the horizontal axis, output vertically, and evenly spaced numerical scales. A line segment preserves a bounded continuous domain; discrete allowed inputs may require points rather than every intervening value.
Original case: V=4+3t for 0≤t≤4; liters versus elapsed minutes.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Original case: V=4+3t for 0≤t≤4; liters versus elapsed minutes. |
Copy as plain text
1. 1. Label axes
Name both axes and their units.
You should see: Horizontal: t/min; vertical: V/L.
2. 2. Plot checked points
Calculate and mark t=0,2,4.
You should see: Points (0,4),(2,10),(4,16).
3. 3. Choose the display
Join points only over the allowed continuous time interval.
You should see: A straight segment from (0,4) to (4,16).
4. 4. Read a new point
Use the rule or segment to find V at t=3.
You should see: V(3)=13 L; it lies between the neighboring plotted values.
What to finish
A labeled graph with checked points and a domain-aware segment or point set.
Watch for this
The graph should respect the allowed domain.
How can I tell I understand it?
Plot a new input correctly and avoid implying prohibited intermediate values.
Quick knowledge check
Answer all 3 questions. Get at least 2 right and the lesson completes automatically.
You’ll get an explanation for each answer. Signed in? Your results save to your account.
Pass the check. We’ll save the progress.
Answer all 3 questions above and get at least 2 right. You can review the explanations and try again.
Go to the knowledge checkTools, templates, and lesson sources
Tools and templates
Tools open in a new tab so you can keep your place here.
Sources and further reading
Explore the references behind this lesson.
Source & access notes · checked 2026-10-01
Web open/search showed the official page, its topic heading and relevant concept description. This is a content/source check, not a provider endorsement. Exact topic chapters were opened in web result turn 325view 0–14.
Access: Official page retrieved with the web reader on 2026-10-01; interactive tools and videos were not certified by retrieval.
Reuse: Original fictional teaching cases, calculations, questions and examples; link and short factual paraphrase only. No copied source exercises or illustrations.
Source & access notes · checked 2026-10-01
Web open/search showed the official page, its topic heading and relevant concept description. This is a content/source check, not a provider endorsement.
Access: Official page retrieved with the web reader on 2026-10-01; interactive tools and videos were not certified by retrieval.
Reuse: Original fictional teaching cases, calculations, questions and examples; link and short factual paraphrase only. No copied source exercises or illustrations.
Report a problem with this lesson
Tell us what went wrong. Please leave out personal information and private project contents.