Week 4 — Quiz (auto-graded) · Linear Functions & Their Graphs

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective tested: Objective 4 — slope; slope-intercept and point-slope forms; intercepts; parallel and perpendicular lines; horizontal and vertical lines; interpreting slope in context.
Points: 10 (1 each) · Assignment group: Quizzes (15% of grade) · Due: end of Module 4.

This is the human-readable quiz with its vetted answer key and feedback. The import-ready Classic QTI is in F-quiz-week-04-qti.xml. AI is not permitted on quizzes (course AI policy). Every numeric answer below is pre-computed and independently re-verified (Python w04_verify.py, PASS).

Blueprint

No trick questions; distractors target the Week 4 misconceptions named in the lecture outline (swapping rise/run, sign errors on slope, confusing the negative with the negative reciprocal, undefined vs. zero slope, swapping m and b).

Questions, key, and feedback

Q1 (MC). What is the slope of the line through (1, 2) and (4, 11)?
- A. 1/3
- B. 3 ✅
- C. −3
- D. 9
Feedback: slope = (y₂ − y₁)/(x₂ − x₁) = (11 − 2)/(4 − 1) = 9/3 = 3. (A = flipped rise and run; C = correct numerics but wrong sign; D = only the rise, forgot to divide by the run.)

Q2 (MC). Identify the slope m and y-intercept b of the line y = −2x + 5.
- A. m = 5, b = −2
- B. m = 2, b = 5
- C. m = −2, b = 5 ✅
- D. m = −2, b = −5
Feedback: in y = mx + b, the slope is always the coefficient of x (−2) and b is always the constant term (5). (A = classic swap of m and b; B = dropped the negative on slope; D = wrong sign on b.)

Q3 (MC). A line has slope 3 and passes through the point (2, 1). Which equation represents this line?
- A. y = 3x + 7
- B. y = 3x − 5 ✅
- C. y = 3x + 1
- D. y = 3x + 2
Feedback: point-slope: y − 1 = 3(x − 2) → y = 3x − 6 + 1 = 3x − 5. Check: 3(2) − 5 = 1 ✓. (A = added 1 + 6 instead of 1 − 6; C = used the y-coordinate as b directly without point-slope; D = used the x-coordinate as b.)

Q4 (MC). Which equation passes through (0, 4) and (2, 10)?
- A. y = 3x + 2
- B. y = 3x + 4 ✅
- C. y = 6x + 4
- D. y = 3x − 4
Feedback: slope = (10 − 4)/(2 − 0) = 6/2 = 3; y-intercept = 4 (from the point (0, 4)) → y = 3x + 4. (A = wrong intercept; C = forgot to divide rise by run; D = sign error on intercept.)

Q5 (MC). What is the slope of a line parallel to y = 4x − 1?
- A. 4 ✅
- B. −4
- C. 1/4
- D. −1/4
Feedback: parallel lines have equal slopes. The slope of y = 4x − 1 is 4, so any parallel line also has slope 4. (B–D are various perpendicular or reciprocal values — none apply to a parallel line.)

Q6 (MC). What is the slope of a line perpendicular to y = (2/3)x + 1?
- A. 2/3
- B. −2/3
- C. 3/2
- D. −3/2 ✅
Feedback: the perpendicular slope is the negative reciprocal: flip 2/3 → 3/2, then change the sign → −3/2. Verify: (2/3)(−3/2) = −1 ✓. (B = only changed the sign; C = only flipped the fraction; A = the original slope unchanged.)

Q7 (MC). Find the x-intercept of 2x + 3y = 12.
- A. (0, 4)
- B. (4, 0)
- C. (0, 6)
- D. (6, 0) ✅
Feedback: x-intercept → set y = 0: 2x + 3(0) = 12 → 2x = 12 → x = 6 → point (6, 0). (A = the y-intercept (set x = 0 instead); B = divided 12 by 3 instead of 2; C = gives coordinates with x and y swapped.)

Q8 (MC). What is the slope of the vertical line x = 5?
- A. 5
- B. 0
- C. 1/5
- D. Undefined ✅
Feedback: on a vertical line, every point has the same x-value, so the run (Δx) is always 0. Slope = rise/0 → undefined (division by zero). (B = slope 0 describes a horizontal line, not a vertical one; A and C are numerical misconceptions.)

Q9 (Matching). Match each equation to the description that best fits it.

Pairs:
- y = 2x − 3 → Slope 2, crosses y-axis below origin (b = −3, so below 0)
- y = −x + 4 → Slope −1, y-intercept 4
- y = 5 → Horizontal line, slope 0
- x = −3 → Vertical line, undefined slope

Feedback: read m directly as the x-coefficient and b as the constant; "y = constant" is horizontal (slope 0); "x = constant" is vertical (undefined slope).

Q10 (MC). A rideshare ride costs C = 0.5m + 20 dollars, where m is miles driven. What does the slope 0.5 represent?
- A. The total cost of the ride
- B. The base fee before driving any miles
- C. The cost per mile driven ✅
- D. The number of miles in a typical trip
Feedback: in a linear model y = mx + b, the slope m is the rate of change — the amount y changes per unit of x. Here, slope = 0.5 means the cost increases \$0.50 per mile. The 20 is the y-intercept, not the slope. (B = that's the y-intercept (base fee); A and D are not what slope represents.)

Answer key (quick reference)

Quality gate (self-checked, computer-verified): each single-answer item has exactly one correct option; matching pairs 4:4 one-to-one. Arithmetic pre-computed and independently re-verified (w04_verify.py, PASS): Q1 9/3 = 3; Q3 3(2)−5 = 1 ✓; Q4 slope (10−4)/(2−0) = 3, intercept = 4; Q6 (2/3)(−3/2) = −1 ✓; Q7 2x = 12 → x = 6; Q10 slope = rate = $0.50/mile. All checks PASS. QTI parse confirmation: F-quiz-week-04-qti.xml parses as imsqti_xmlv1p2 with 10 items.

Item-bank entries (for variants + the midterm/final)

All ten items are tagged course=MATH120 · week=4 · objective=4 · topic=linear-functions-graphs and deposited in Item Bank: Week 4 — Linear Functions & Graphs. The midterm (Week 8) and per-term variant updates draw fresh items from this bank. (Tags: q1 slope-two-points, q2 read-slope-intercept, q3 point-slope-form, q4 slope-intercept-two-points, q5 parallel-slope, q6 perpendicular-slope, q7 x-intercept, q8 vertical-slope, q9 matching-line-features, q10 interpret-slope-context.)

Canvas placement block

canvas_object   = Quizzes::Quiz
title           = "Week 4 Quiz — Linear Functions & Their Graphs"
assignment_group = "Quizzes"
points_possible = 10
grading_type    = points
due_offset_days = 6        # 6 days after module start (Sun Sep 27)
published       = true
shuffle_answers = true
provenance      = "~ Prof. Calloway's edition · Fall 2026 · built with thecoursemaker.com"