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Week 4 · Assignment: Traditional alternative (no AI)

Week 4 — Reading Lines: A Short Line Report — Traditional alternative (no AI)

College Algebra Free sample edition
Traditional alternative (no AI), unpublished. In the course this is a separate assignment that ships unpublished beside the adaptive assignment: same objective, no AI. An instructor who prefers it publishes it and unpublishes or deletes the adaptive one, as the note at its top says.

Instructors: publish this instead of the adaptive version if you prefer, and unpublish or delete the adaptive one.

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 week you learned to find a slope as rise over run, to read slope-intercept form, to build a line from two points with point-slope form, to find intercepts from standard form, and to compare parallel and perpendicular lines. 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. In this assignment you work four short problems, interpret each one, and explain to someone who has never studied algebra what the two numbers in a price line mean. This week's lecture tutorial, quiz, discussion, and Model/Build Studio practise the same ideas from other angles.

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.

Show your arithmetic. A reader should be able to reproduce every number you report from the values above without guessing which values or steps you used.

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.

Deliverables

Submit a single line report containing:

  • the four answers, each with the arithmetic shown and a brief interpretation of what that value shows about the line and one use or limit of it;
  • your message for the bowl-shop counter, explaining what the 3 and the 4 in y = 3x + 4 mean, how to find a price, and one honest limit; and
  • a one-line restatement of the values you used, so your results are reproducible.

Keep it to roughly one page. Clear and correct beats long.

Choose how you show it. Present your report as written text, or as a recorded audio or video explanation of about three minutes with a transcript, or as a labelled sketch of the lines with a short note. Every form is graded by the same scoring criteria. 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.

How you'll be graded

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

Academic integrity and AI use

This version is designed to be completed without AI: do the computations, the interpretations, and the writing yourself, without a chatbot or other AI tool. You may use a calculator or a free graphing calculator such as Desmos to check your arithmetic and your lines. Submitting AI-generated work as your own, or copying another student's numbers, is an integrity violation under the course policy.

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