Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Module: Week 4 of 16 · Fall 2026 · in-person, two 75-minute sessions
Objective covered: Objective 4 — Analyze and graph linear functions using slope, intercepts, and the slope-intercept, point-slope, and standard forms; identify parallel and perpendicular lines.

This file holds two pieces: (A) the Module 4 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. Dates below assume a Tuesday/Thursday session pattern with Week 4 meeting Tue Sep 22 and Thu Sep 24, and end-of-week work due Sunday Sep 27, 11:59 p.m. Adjust the day-of-week and times to match your section. (Module start: Mon Sep 21, 2026 — no campus holidays this week.)

(A) Module 4 Overview — Start Here

Welcome to Week 4: Linear Functions & Their Graphs

This is your home base for the week. Read it first, then work the checklist below from top to bottom. Everything you need is linked inside the module.

Three weeks in, you can evaluate expressions, solve equations, and work with functions. This week we add a picture to the story: you'll learn to read the slope of a line the way you read speed on a speedometer — instantly, at a glance, with total confidence. Every linear relationship you'll ever model (cost, distance, temperature, revenue) lives on a graph you can now build and interpret from scratch.

The week's big question

"What does the steepness of a line tell you — and how do you build a line from as little as one point and a slope?"

By Sunday you'll compute slope, write equations in slope-intercept and point-slope form, find x- and y-intercepts, and tell parallel from perpendicular at a glance — even when the line is horizontal, vertical, or upside down.

By the end of this week, you can…

Use this as a checklist. If you can do all four, you're ready for the quiz.

• [ ] Compute slope from two points using m = (y₂ − y₁)/(x₂ − x₁), and read m and b directly from y = mx + b.
• [ ] Write the equation of a line in slope-intercept or point-slope form, given a point and slope or two points.
• [ ] Find x- and y-intercepts and sketch a line using them; recognize that a horizontal line has slope 0 and a vertical line has undefined slope.
• [ ] Identify parallel lines (equal slopes) and perpendicular lines (slopes that multiply to −1, i.e., negative reciprocals).

What's due this week, and when

Work these in order — each one gets you ready for the next.

Heads-up on the AI tutorial: you'll use a chatbot to draft, and then you judge its work. Chatbots are especially prone to mixing up perpendicular slope (they confuse "negative" with "negative reciprocal") and to getting sign errors in point-slope form. Catching the model is the point.

Late policy reminder: 10% off per day late. If life happens, reach out before the deadline — I'd much rather hear from you early.

How to succeed this week

• Learn slope by counting, not by plugging. Before you use the formula, draw the two points, count the rise, count the run, and check the sign. Formula + picture = foolproof.
• Memorize the two traps. Perpendicular slope is the negative reciprocal, not just the negative (flip AND change sign), and vertical lines have undefined slope, not 0 (that's horizontal). These two cause most Week-4 lost points.
• Point-slope is your Swiss Army knife. One point and one slope → any line. Slope-intercept is just what you get after you simplify — you don't have to start there.
• Use Desmos to check every graph. Type y = 3x - 5 and see it instantly; type two equations and watch whether they're parallel, perpendicular, or neither. That visual feedback is the fastest way to catch a sign error.
• Context is king on the assignment. When the slope is 0.5 and the units are dollars per mile, say "dollars per mile" — the number alone is half-credit.

You have three weeks of solid algebra under your belt. This week you're going to see it. See you Tuesday.

(B) Welcome Announcement — Module 4

Release setting: post on the module's start day (offset = 0 days), i.e., Mon Sep 21, 2026 — not before. If your platform won't preserve the scheduled date on import, post this as a draft labeled "Release: Mon Sep 21."

Subject: Week 4 — let's see what algebra looks like 📈

Hi everyone,

Quick question: have you ever looked at a phone bill and thought "the more I use, the more I pay — but how much more?" That's a linear function. This week we stop just solving for x and start drawing and reading the algebra — and once you can read a line, you can build a model for almost anything that changes at a steady rate.

This week — Linear Functions & Their Graphs — we tackle the big question: What does the steepness of a line tell you, and how do you build a line from one point and a slope? By Friday you'll compute slope from two points, write the equation of any line in two forms, find where a line crosses the axes, and immediately recognize parallel and perpendicular lines just by comparing slopes.

Three things not to miss:
1. Lecture Tutorial 4 — work through slope, line forms, intercepts, and parallel/perpendicular with one approved chatbot (Gemini, Claude, or ChatGPT) and submit the share link. The chatbot almost always mixes up "perpendicular slope" — catching that is the whole exercise. Due Sun Sep 27.
2. Quiz 4 (no AI on quizzes) and Discussion 4 — the discussion is about a real-world linear relationship you find yourself, so start that early and leave time to reply to classmates. Both close Sun Sep 27.
3. Assignment 4 — four AI-coached problems with a self-scored report, including a real-world modeling problem; due Sun Sep 27.

One tip for the week: any time you write a line equation, plug your answer back in to check that the original point satisfies it. Thirty seconds, total, and it catches almost every error. Bring pencil and graph paper (or Desmos) on Tuesday.

See you soon,
Prof. Calloway