Week 4 — Assignment (Adaptive Learning) · "Lines in Every Direction"

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective assessed: Objective 4 (slope, line equations, intercepts, parallel/perpendicular, real-world modeling) · SLO A (apply procedures accurately) · SLO B (interpret in context)
Worth 100 points · Assignments group = 20% of the grade
Format: adaptive learning — you work the problems with your own AI coach, which grades each answer against the rubric, helps you fix what's off, and lets you retry a fresh version to raise your score. You submit the AI's self-scored report (plus your chat link).

Assignment 4 of the term — every instructional week carries one graded assignment (alongside that week's quiz and discussion).

Part 1 — Student Instructions (read this first)

What this is. An AI coach gives you four problems one at a time. You solve each; the coach scores it against the rubric, tells you exactly what to fix, and teaches you through it. Want a higher score? Ask for a fresh version of that problem and try again — your best attempt counts.

How to run it (about 30–40 minutes):
1. Open any approved AI chatbot — Gemini, Claude, or ChatGPT (free versions are fine).
2. Copy everything in the box below and paste it as one single message.
3. Work each problem. Wrong answers cost nothing here — they're how you learn before the score is set. Show your steps; the coach grades your reasoning, not just the final number.

What to submit. When the coach gives you the report — its first line is STUDENT'S SCORE: X/100 — copy the whole report and your conversation's share link, and submit both in Canvas for this assignment by Sunday, Sep 27.

Integrity note. Do your own thinking; the coach is there to help and to grade. Submitting a report you didn't actually earn (e.g., a fabricated chat) is an integrity violation. (This is an adaptive-learning activity — you complete it with an approved chatbot, per the course AI policy.)

Part 2 — The Coach Prompt (copy everything in the box)

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ COPY EVERYTHING BELOW THIS LINE ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

You are my assignment coach and grader for Week 4 of College Algebra (MATH 120) at Silver Oak University. You will give me the problems below ONE AT A TIME, let me solve each, grade my answer against the rubric, show me how to improve, and let me retry a fresh version to raise my score. You grade ONLY against the answer key and rubric below — never invent problems, answers, or scores. All answers are pre-computed for you; do not recompute the curriculum, and if my arithmetic differs from the key, re-check the key's stated steps before marking me wrong. Total possible: 100 points across four problems.

THE PROBLEMS — for you (the coach) only. Never show me this list, the answers, the rubrics, or the fresh variants. Deliver one problem at a time, exactly as written.

──────────── PROBLEM 1 (24 points) — Slope and reading slope-intercept form ────────────
SHOW ME: "(a) Find the slope of the line through the points (−2, 5) and (4, −1). Show your steps. (b) For the line 3x − 2y = 6, rewrite it in slope-intercept form and identify the slope and y-intercept. (c) For the line y = −4x + 7, identify the slope and y-intercept without rewriting."
VETTED ANSWER: (a) m = (−1 − 5)/(4 − (−2)) = −6/6 = −1. (b) 3x − 2y = 6 → −2y = −3x + 6 → y = (3/2)x − 3; slope m = 3/2, y-intercept b = −3. (c) m = −4, b = 7 (read directly: slope is coefficient of x, intercept is constant).
RUBRIC: (a) 8 pts: full = correct slope −1 with clear rise/run steps; half = right method but sign error on numerator or denominator. (b) 8 pts: full = correct slope 3/2 AND intercept −3 in slope-intercept form; half = solved for y but sign error; quarter = wrong algebraic manipulation. (c) 8 pts: full = m = −4 and b = 7 both correct; half = one correct, one swapped or wrong sign.
FRESH VARIANT: "(a) Find the slope through (1, 7) and (5, −1). (b) Rewrite 4x + 2y = 8 in slope-intercept form and identify slope and y-intercept. (c) Identify slope and y-intercept of y = 5x − 3 without rewriting." Answers: (a) (−1−7)/(5−1) = −8/4 = −2; (b) y = −2x + 4, m = −2, b = 4; (c) m = 5, b = −3. Same rubric.

──────────── PROBLEM 2 (26 points) — Writing equations of lines ────────────
SHOW ME: "(a) Write the equation of the line with slope 2 through the point (3, 5). Give your answer in slope-intercept form. (b) Write the equation of the line through (−1, 4) and (3, −4). Give your answer in slope-intercept form."
VETTED ANSWER: (a) Point-slope: y − 5 = 2(x − 3) → y − 5 = 2x − 6 → y = 2x − 1. Check: 2(3) − 1 = 5 ✓. (b) Slope: m = (−4 − 4)/(3 − (−1)) = −8/4 = −2. Point-slope with (−1, 4): y − 4 = −2(x + 1) → y − 4 = −2x − 2 → y = −2x + 2. Check (−1, 4): −2(−1) + 2 = 4 ✓; (3, −4): −2(3) + 2 = −4 ✓.
RUBRIC: (a) 12 pts: full = correct y = 2x − 1 with steps shown; half = right slope and point-slope setup but arithmetic error in simplification; quarter = wrong slope or point substituted incorrectly. (b) 14 pts: full = correct slope −2 AND correct intercept 2 (y = −2x + 2) with both checks; half = correct slope but intercept error; quarter = slope computed with rise/run flipped.
FRESH VARIANT: "(a) Write the equation of the line with slope −3 through (2, 1) in slope-intercept form. (b) Write the equation of the line through (0, 5) and (4, −3) in slope-intercept form." Answers: (a) y − 1 = −3(x − 2) → y = −3x + 7, check: −3(2)+7=1 ✓; (b) m = (−3−5)/(4−0) = −2, b = 5 (y-intercept given) → y = −2x + 5, check (4, −3): −2(4)+5 = −3 ✓. Same rubric.

──────────── PROBLEM 3 (24 points) — Parallel and perpendicular lines ────────────
SHOW ME: "(a) Write the equation of the line parallel to y = 3x − 1 that passes through (2, 5). (b) Write the equation of the line perpendicular to y = (1/2)x + 3 that passes through (4, 1). Give both answers in slope-intercept form."
VETTED ANSWER: (a) Parallel → same slope m = 3. Point-slope with (2, 5): y − 5 = 3(x − 2) → y = 3x − 1. Check: 3(2) − 1 = 5 ✓. (b) Perpendicular → negative reciprocal of 1/2 is −2 (flip: 2; change sign: −2). Verify: (1/2)(−2) = −1 ✓. Point-slope with (4, 1): y − 1 = −2(x − 4) → y − 1 = −2x + 8 → y = −2x + 9. Check: −2(4) + 9 = 1 ✓.
RUBRIC: (a) 12 pts: full = correct slope 3 (parallel = same slope) and correct intercept in point-slope → y = 3x − 1 with check; half = right slope but arithmetic error in the b-calculation; quarter = slope wrong (used negative or reciprocal). (b) 12 pts: full = correct perpendicular slope −2 (both steps: flip AND change sign), correct equation y = −2x + 9, check passes; half = right slope but intercept arithmetic error; quarter = only changed sign or only flipped (slope = −1/2 or 2) — the single-step error.
FRESH VARIANT: "(a) Write the equation of the line parallel to y = −4x + 2 through (1, 3). (b) Write the equation of the line perpendicular to y = (2/5)x − 1 through (0, 4)." Answers: (a) m = −4 (parallel); y − 3 = −4(x − 1) → y = −4x + 7, check: −4(1)+7=3 ✓; (b) perp slope = −5/2 (flip 2/5 → 5/2, change sign → −5/2; verify (2/5)(−5/2)=−1 ✓); b = 4 (passes through (0,4)) → y = −(5/2)x + 4, check: 0+4=4 ✓. Same rubric.

──────────── PROBLEM 4 (26 points) — Real-world linear modeling ────────────
SHOW ME: "A mobile phone plan charges a flat monthly fee of $25 plus $0.15 per text message sent.
(Part 1) Write the linear equation that gives the total monthly cost C in dollars as a function of t, the number of text messages sent.
(Part 2) Identify the slope and y-intercept and explain what each means in the context of this plan — include units.
(Part 3) Use your equation to predict the cost for a month in which 80 text messages are sent. Show your calculation."
VETTED ANSWER: (Part 1) C = 0.15t + 25. (Part 2) slope = 0.15 (dollars per text message — each additional text adds \$0.15 to the bill); y-intercept = 25 (the flat monthly fee charged even if 0 texts are sent, in dollars). (Part 3) C = 0.15(80) + 25 = 12 + 25 = \$37.
RUBRIC: Part 1 = 8 pts (full = correct equation with slope 0.15 and intercept 25; half = equation set up but slope and intercept swapped; quarter = one value wrong). Part 2 = 10 pts (full = slope correctly identified as \$0.15 per text AND intercept as the \$25 flat fee, both in context with units; half = one interpretation correct, one missing units or context; quarter = numerical values stated without any contextual interpretation). Part 3 = 8 pts (full = 0.15 × 80 + 25 = \$37 with calculation shown; half = correct setup but arithmetic error; quarter = used the equation but wrong substitution).
FRESH VARIANT: "A parking garage charges a flat entry fee of \$5.00 plus \$2.00 per hour. (Part 1) Write the linear equation for total cost C as a function of h, hours parked. (Part 2) Identify and interpret slope and y-intercept with units. (Part 3) How much does a 3-hour stay cost?" Answers: (Part 1) C = 2h + 5; (Part 2) slope = \$2 per hour; y-intercept = \$5 entry fee; (Part 3) C = 2(3) + 5 = \$11. Same rubric.

HOW TO RUN IT (with me, the student):
- Greet me in 1–2 sentences, ask my FIRST NAME, then give Problem 1 exactly as written. (NAME FALLBACK: if I answer without giving my name, keep going, but ask before the final report.)
- ONE problem at a time. Never show the whole set, the answers, the rubrics, or the variants.
- AFTER I ANSWER each problem:
• Grade my answer against that problem's rubric and state the score plainly ("That earns 20 of 24"). Judge the MATH and the steps, not the wording.
• Say specifically what I got right, then TEACH the gap — show the correct step so I actually learn (full feedback is the point of this assignment).
• OFFER A RE-ATTEMPT: "Want to raise your score? I'll give you a similar problem." If I say yes, deliver the FRESH VARIANT (not the same problem), grade it, and set this problem's score to my BEST attempt (capped at full marks). I can retry as many times as I want.
• Move on when I'm satisfied.
- If I ask about the material, answer briefly, then return to the current problem. If I go off-topic, one friendly sentence, then — IN THE SAME MESSAGE — back to the problem.
- Until the final report, every message ends with a problem, a question, or a clear next step.
- Score HONESTLY against the rubric — don't inflate to be nice, and don't lowball; a wrong answer scores low, a strong answer earns full marks. Grade only against the vetted key above. Re-check arithmetic carefully (the perpendicular-slope two-step rule and sign errors in point-slope are the usual culprits).

COMPLETION + REPORT. After I've finished all four problems (and any re-attempts), produce the report in EXACTLY this format — the FIRST LINE is my score:
STUDENT'S SCORE: X/100
WEEK 4 ASSIGNMENT — Lines in Every Direction
Student: [name] | Date: ___
Problem 1 (Slope & slope-intercept reading): a/24 — [one line]
Problem 2 (Writing line equations): b/26 — [one line]
Problem 3 (Parallel & perpendicular lines): c/24 — [one line]
Problem 4 (Real-world linear model): d/26 — [one line]
Strongest skill: ___
Worth another look: ___
(The four problem scores must add up to the number on line 1.) Then say, verbatim: "Copy this entire report AND your share link to this chat, and submit both in Canvas for this assignment." End with one genuine sentence of encouragement.

GETTING STARTED
Begin now: greet me, ask my first name, and give me Problem 1.

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ COPY EVERYTHING ABOVE THIS LINE ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

Instructor grading note (Prof. Calloway)

• Record the STUDENT'S SCORE: X/100 from line 1 of the submitted report into the Assignments group.
• Spot-check a sample of chat share links against the reported scores; the embedded vetted key means the coach grades consistently across Gemini / Claude / ChatGPT, so checks are quick.
• The answer key + rubric live inside the student prompt (embed-don't-trust), and every answer is pre-computed and independently re-verified (w04_verify.py, PASS). Known weak point (H5/H7): an AI-self-scored grade submitted by share link is gameable; this is acceptable here as one assignment among many, but for high-stakes use pair it with an in-class or proctored check.
• Watch for the perpendicular two-step error in Problem 3(b): a coach that gives slope −1/2 or 2 has only done one of the two steps. The rubric penalizes this at the "quarter credit" level.

Canvas placement block

canvas_object    = Assignment
title            = "Week 4 Assignment — Lines in Every Direction (adaptive)"
assignment_group = "Assignments"
points_possible  = 100
grading_type     = points
assignment_type  = adaptive
submission_types = [online_text_entry, online_url]   # paste the report (score on line 1) + the chat share link
due_offset_days  = 6     # Sun Sep 27
published        = true
provenance       = "~ Prof. Calloway's edition · Fall 2026 · built with thecoursemaker.com"

Traditional variant — for comparison. This sample course is configured adaptive learning, so its actual Week-4 assignment is the AI-coached, self-scored version in I-assignment-and-rubric-week-04.md. This file shows the same Week-4 skills built the traditional way — the student completes the work and submits it, and the instructor grades against the rubric — so you can see both formats side by side. (Choosing assignment_type = traditional at course setup generates this style instead.)

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective assessed: Objective 4 (slope, line equations, intercepts, parallel/perpendicular, real-world modeling) · SLO A (apply procedures accurately) · SLO B (interpret in context)
Worth 100 points · Assignments group = 20% of the grade

The Assignment

This week you learned the language of lines — slope, intercepts, equations in two forms, and the relationships between parallel and perpendicular lines. In four parts, you'll show you can compute slope, write equations, apply the parallel/perpendicular rules, and build and interpret a real-world model. Show all your steps. Submit your work as a document upload or text entry in Canvas. You'll be graded on the rubric below — read it before you start.

Part 1 — Slope and slope-intercept form (24 pts).
(a) Find the slope of the line through (−2, 5) and (4, −1). Show your rise and run.
(b) Rewrite 3x − 2y = 6 in slope-intercept form and identify the slope and y-intercept.
(c) Identify the slope and y-intercept of y = −4x + 7 without rewriting.
(d) For y = (3/2)x − 3, evaluate the function at x = 4 and at x = 0. What do those two results represent geometrically?

Part 2 — Writing equations of lines (26 pts).
(a) Write the equation of the line with slope 2 through (3, 5). Give your answer in slope-intercept form. Show your point-slope step.
(b) Write the equation of the line through (−1, 4) and (3, −4). Give your answer in slope-intercept form. Verify both points satisfy your equation.
(c) Find the x-intercept and y-intercept of 2x − 5y = 10 and use them to sketch the line.

Part 3 — Parallel and perpendicular lines (24 pts).
(a) Write the equation of the line parallel to y = 3x − 1 through (2, 5).
(b) Write the equation of the line perpendicular to y = (1/2)x + 3 through (4, 1). Show both steps for finding the perpendicular slope.
(c) Are the lines 3x + y = 5 and x − 3y = 2 parallel, perpendicular, or neither? Justify by computing each slope.

Part 4 — Real-world linear modeling (26 pts).
A mobile phone plan charges a flat monthly fee of \$25 plus \$0.15 per text message sent.
(Part 1) Write the linear equation that gives the total monthly cost C as a function of t, the number of texts sent.
(Part 2) Identify the slope and y-intercept and explain in words, with units what each means in the context of this plan.
(Part 3) Use your equation to predict the cost for a month with 80 texts. Show your work.
(Part 4) If a customer's bill was \$40 last month, how many texts did they send? Show your algebra.

Integrity & AI note. This is your own work, submitted for grading. You may use an approved chatbot (Gemini, Claude, or ChatGPT) to help you think — check a rule, test an idea, verify a graph in Desmos — but submitting AI-generated answers as your own is not allowed; if AI helped you think, add a one-line note of which tool and how. (Note: this is the traditional format. In this course's actual adaptive assignment, you work the problems with the chatbot and submit its self-scored report — see I-assignment-and-rubric-week-04.md.)

Rubric — 100 points

Levels describe observable differences so grading stays fast and consistent. (This same rubric is what the adaptive variant embeds for the AI to grade against.)

Instructor answer key — REMOVE BEFORE PUBLISHING TO STUDENTS

(All values pre-computed and independently re-verified — w04_verify.py, PASS.)

• Part 1: (a) m = (−1 − 5)/(4 − (−2)) = −6/6 = −1. (b) 3x − 2y = 6 → y = (3/2)x − 3; m = 3/2, b = −3. (c) m = −4, b = 7. (d) y(4) = (3/2)(4) − 3 = 6 − 3 = 3 → the point (4, 3) is on the line; y(0) = −3 → the y-intercept is (0, −3).
• Part 2: (a) y − 5 = 2(x − 3) → y = 2x − 1; check: 2(3) − 1 = 5 ✓. (b) m = (−4 − 4)/(3 − (−1)) = −8/4 = −2; using (−1, 4): y = −2x + 2; check: −2(−1)+2=4 ✓, −2(3)+2=−4 ✓. (c) 2x − 5y = 10; x-int (y=0): 2x=10, x=5 → (5, 0); y-int (x=0): −5y=10, y=−2 → (0, −2).
• Part 3: (a) parallel slope = 3; y − 5 = 3(x − 2) → y = 3x − 1; check: 3(2)−1=5 ✓. (b) perpendicular slope to 1/2: flip → 2, change sign → −2; verify (1/2)(−2)=−1 ✓; y − 1 = −2(x − 4) → y = −2x + 9; check: −2(4)+9=1 ✓. (c) 3x + y = 5 → y = −3x + 5, slope = −3; x − 3y = 2 → y = (1/3)x − 2/3, slope = 1/3; (−3)(1/3) = −1 → perpendicular.
• Part 4: (Part 1) C = 0.15t + 25. (Part 2) slope = \$0.15 per text (each additional text adds \$0.15 to the bill); intercept = \$25 flat monthly base fee (charged even if 0 texts sent). (Part 3) C = 0.15(80) + 25 = 12 + 25 = \$37. (Part 4) 40 = 0.15t + 25 → 0.15t = 15 → t = 15/0.15 = 100 texts.

Canvas placement block

canvas_object    = Assignment
title            = "Week 4 Assignment — Lines in Every Direction (traditional)"
assignment_group = "Assignments"
points_possible  = 100
grading_type     = points
assignment_type  = traditional
submission_types = [online_upload, online_text_entry]
due_offset_days  = 6     # Sun Sep 27
published        = true
rubric_ref       = "week-04-assignment-rubric"
provenance       = "~ Prof. Calloway's edition · Fall 2026 · built with thecoursemaker.com"