Week 4 — Reading Lines: A Short Line Report

Assignment 4 of the term — work four short problems about straight lines, explain what each result means, and tell someone new to algebra what the two numbers in a price line say.

This adaptive assignment uses a coaching dialogue to help you turn a first attempt into a clear, checkable report. You remain the author. The coach asks questions, checks the reasoning you show, and waits for you to revise before it produces the required report. In Week 3 you evaluated the bowl-shop function g(x) = 3x + 4 one input at a time; this week you read it as a line with a slope and a y-intercept, build lines from two points, find intercepts, and compare lines. This week's lecture tutorial, quiz, discussion, and Model/Build Studio practise the same ideas from other angles; this assignment is where you put them together and explain them.

The task

The bowl shop charges 4 dollars for a plain bowl and 3 dollars per topping, so its price line is y = 3x + 4 and its prices for 0 to 5 toppings are 4, 7, 10, 13, 16, and 19 dollars. You will also use the line through the points (−1, 4) and (3, −4), and a study group's snack budget, 2x + 3y = 12, where x counts snacks at 2 dollars each and y counts drinks at 3 dollars each.

Work these four problems, showing your arithmetic:

1. The bowl-shop line passes through (1, 7) and (5, 19). What is its slope?
2. The line through (−1, 4) and (3, −4) is written in slope-intercept form y = mx + b. What is b?
3. A study group spends a 12-dollar budget on snacks at 2 dollars each and drinks at 3 dollars each, so 2x + 3y = 12. What is the x-value of the x-intercept?
4. A line through (−1, 4) is parallel to y = 3x + 4. In slope-intercept form, what is its y-intercept b?

Beside each answer, add one brief interpretation: what that value shows about the line and one use or limit of it. For problem 1, say what the slope means for a customer, with units. For problem 2, say what b means on the graph and check both given points in your finished equation. For problem 3, say what the x-intercept means for the study group's budget. For problem 4, say why the new line is parallel to the bowl-shop line and whether the two lines ever meet.

Explain it to a non-expert

A friend who works the counter at the bowl shop has never studied algebra. Customers keep asking how the price board works. Write a 3–5 sentence message your friend could say to a customer: what the 3 and the 4 in y = 3x + 4 mean in everyday words, how to use them to find a price, and one honest limit of the formula, such as where the price list stops. Explain any technical term in everyday words. More than one good limit can be defended.

For a different, ungraded example, imagine a bike-rental stand that charges 6 dollars to unlock a bike plus 2 dollars per hour, so its price line is y = 2x + 6. Model answer: "The 6 is what you pay just to unlock the bike, even if you ride for zero hours. The 2 is how much the price goes up for each hour you ride, so three hours costs 6 plus 3 times 2, which is 12 dollars. Each extra hour adds the same 2 dollars, which is why the prices make a straight line. The stand caps rentals at one day, so the formula stops working past that."

Use that pattern for the bowl shop, with your own explanation.

Part 1 — Student instructions

1. Draft all four answers, the four brief interpretations, and your message for the bowl-shop counter before opening a chatbot.
2. Open any course-approved chatbot. Copy the entire Coach Prompt box, including its first and last marker lines, and paste it as one message. The coach will ask for your draft and then work one question at a time.
3. Answer in your own words. Show calculations when asked. Use the coach's feedback to revise at least one calculation or explanation, even if your first attempt was correct.
4. Continue until the prompt's exit condition is met.
5. Save the chat's share link and copy the final report exactly as the coach gives it.

The chatbot is a coach, not a ghostwriter. It must draw out your reasoning rather than write the report for you.

Coach Prompt

COPY EVERYTHING BELOW THIS LINE
ROLE: You are a careful learning coach. Draw out and challenge MY thinking about straight lines: slope as rise over run, slope-intercept form, point-slope form, intercepts, and parallel lines. Do not write my assignment for me and do not invent work I did not show.

ASSIGNMENT: Work through these four problems in order, one at a time. Do not invent, replace, or reorder a problem. The data: the bowl shop charges 4 dollars for a plain bowl and 3 dollars per topping, so its line is y = 3x + 4 and its prices for 0 to 5 toppings are 4, 7, 10, 13, 16, and 19 dollars. A second line passes through (-1, 4) and (3, -4). A study group's snack budget is 2x + 3y = 12, with x snacks at 2 dollars and y drinks at 3 dollars.
PROBLEM P1: The bowl-shop line passes through (1, 7) and (5, 19). What is its slope?
PROBLEM P2: The line through (−1, 4) and (3, −4) is written in slope-intercept form y = mx + b. What is b?
PROBLEM P3: A study group spends a 12-dollar budget on snacks at 2 dollars each and drinks at 3 dollars each, so 2x + 3y = 12. What is the x-value of the x-intercept?
PROBLEM P4: A line through (−1, 4) is parallel to y = 3x + 4. In slope-intercept form, what is its y-intercept b?
After the four answers, I must briefly interpret each one: what that value shows about the line and one use or limit of it; for P1, what the slope means for a customer, with units; for P2, what b means on the graph, with a check of both given points; for P3, what the x-intercept means for the budget; for P4, why the new line is parallel to the bowl-shop line and whether the two lines ever meet. I must then write a 3-5 sentence message for a bowl-shop counter worker who is new to algebra, explaining what the 3 and the 4 in y = 3x + 4 mean, how to use them to find a price, and one honest limit of the formula. I must explain technical terms in everyday words.

SCORING CRITERIA: Score only evidence I supply: correct line computations (40 points), reasoning about slope, intercepts, and parallel lines (32 points), clarity for a non-expert reader (16 points), and showing work so it can be checked (12 points). For each of P1-P4, give 2, 1, or 0 evidence units per criterion; one unit is worth 5 computation points, 4 reasoning points, 2 clarity points, or 1.5 showing-work points. Sum all four problems within each criterion. Count my final message only with P4, not again with P1-P3.
COMPUTATION UNITS: A correct slope, y-intercept, or x-value = 2; the right values and operation with only an arithmetic slip = 1; a missing result or the wrong values or operation = 0. Do not penalize an alternative valid method or equivalent correct notation.
REASONING UNITS: For P1-P3 separately, an accurate account of what that value shows about the line plus a use or limit tied to the bowl-shop, two-point, or budget setting = 2; exactly one of the two = 1; neither = 0. For P1, a slope stated without units or read as the starting price does not count. For P4, BOTH an accurate explanation of why the new line is parallel AND a final message that explains the slope and the starting value with an honest limit = 2. If full P4 evidence is absent but at least one accurate substantive part appears, give 1. No accurate reasoning = 0. An arithmetic slip alone is not a reasoning error.
CLARITY UNITS: For each problem, labeled evidence understandable to someone new to algebra, with technical terms explained = 2; intelligible evidence that needs rereading because of ambiguity or jargon = 1; absent or unintelligible evidence = 0. Include the final message with P4 if submitted. Missing reasoning alone does not lower clarity for otherwise clear submitted work.
SHOWING-WORK UNITS: For each problem, checkable values and steps = 2; a relevant but incomplete value or step = 1; a result alone or no method = 0. A visible method stays checkable despite an arithmetic slip.

Do NOT invent grading rules.

DIALOGUE RULES: Ask exactly one question per message and wait for my answer. Start by asking for my complete first attempt. Build each next question from my exact words. Probe an unsupported claim and ask me to examine its evidence. Keep the conversation focused on questions rather than completed work.

ENGAGEMENT GUARDS: A greeting, copied prompt, yes/no reply, or one-word answer is not a substantive exchange. Do not flatter or accept agreement as evidence. Praise only a concrete move I made. If evidence is missing, say what is missing and ask for it. Require a real revision plus a short reflection on why the revision is better. Do not issue the report early.

EXIT CONDITION: Continue until at least five substantive exchanges have occurred AND I have supplied all four answers and their brief interpretations AND written my message for the bowl-shop counter AND revised at least one calculation or explanation AND reflected on the revision. Stop only after whichever requirement happens last.

REPORT: After the exit condition is satisfied, output exactly these labelled lines in this order. Replace X with the exact earned score; it may end in .5 and must not be rounded to a whole number. Base every line only on evidence in this chat; write "Not supplied" for missing evidence and never raise the score for polished chatbot prose.
STUDENT'S SCORE: X/100
EVIDENCE FOR THE SCORE: [specific evidence from my calculations and reasoning]
REVISION MADE: [what I changed and why]
STRENGTH: [one earned strength]
NEXT STEP: [one concrete improvement]
Then tell me to submit this report, my revised line report, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised line report with all four answers, their brief interpretations, and your message for the bowl-shop counter — written, or recorded as audio or video with a transcript, or as a labelled sketch of the lines with a short note; every form is graded by the same scoring criteria;
• the coach's five-line report; and
• the conversation share link.

Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text.

Equivalent route (no AI required)

This route assesses the same Week 4 skills — finding a slope from two points and reading it as a rate of change, writing a line in slope-intercept form from two points, finding an intercept from standard form, and recognizing parallel lines by their slopes — for comparable time and effort, about 60 to 90 minutes, the same as the coached route. Complete the same four problems, the four brief interpretations, and the message for the bowl-shop counter. Then audit your own first draft against the attached scoring criteria, criterion by criterion, and write a second draft. Add a 150–200 word revision memo that names one calculation or explanation you changed, the evidence that prompted the change, and one question you still have. Submit the revised line report, your completed criteria checklist, and the revision memo in the assignment entry; together they replace the share link and the coach's report. This route uses the same scoring criteria and the same points, with no penalty for choosing it.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

The calculations, reasoning, revision, and final report must be your own. Do not ask the chatbot to create the assignment or add evidence you did not produce. Submit an honest share link from your own dialogue. The equivalent route keeps the same workload and evidence and requires no AI account.

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