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Exploring Constant Change — Module Hub & Visuals
A constant rate of change draws a straight line. Move the sliders, watch the line rebuild itself, and see what slope really means.
Lesson Slides & PDFs
Student-facing lesson slide PDFs are grouped by topic below for review, catch-up, and family support.
📖 Student Edition for this module (PDF) ✍ Skills Practice — Student Edition (PDF)
Graphic Organizers & Activities
Foldable notes and activities for each lesson, with the one to start with listed first. Sign in with your alias and PIN to open them.
Start Here — What Module 2 Is About
What this module is for, and what you will be able to do by the end of it.
This is the Module 2 lab bench. The function \(y = mx + b\) is the blueprint of constant change: the slope \(m\) is the rate, and the y-intercept \(b\) is where the story starts. Drag the controls and the graph, the intercepts, the slope triangle, the value table, and a real fare model all update at once — the same move a mathematician makes: change a parameter, read the consequence.
Key Vocabulary
The precise words for what you just investigated. The standards this module carries are in the next section.
Standards in This Module
The Texas Essential Knowledge and Skills this module is built to teach. RDY marks a STAAR readiness standard.
A.2 — Write and represent linear functions from situations, tables, and graphs (slope-intercept form, intercepts).
A.3 — Determine slope and intercepts; graph linear functions; describe how changing m and b transforms a line.
A.4 — Interpret the rate of change and starting value of a linear model in a real context (the fare above).
Process standards A.1A–A.1G — tools, representations, and reasoning — run through every move in this lab.
How to Read the Lab
Two minutes of orientation, then four moves to try. Everything updates live as you drag.
What you're seeing
- Line A (course blue) is your main line, \(y = mx + b\). The slope m slider tilts it; the y-intercept b slider slides it up and down.
- The dashed rise/run triangle shows slope as a ratio: go run right, then rise up. \(m = \frac{\text{rise}}{\text{run}}\).
- The dots mark the y-intercept \((0,\,b)\) — where the line crosses the y-axis — and the x-intercept, where it crosses the x-axis.
- The value table lists exact \((x,\,y)\) pairs; the highlighted row is the y-intercept.
- Open scene 3, Compare two lines, to put a second line beside yours — the readout tells you which is steeper, whether they're equally steep, or whether they're parallel.
Try this
- Set Line A's slope to 2 and read the triangle: run 1, rise 2. Now make m negative — which way does the line tip?
- Hold the slope fixed and drag b from \(-10\) to \(10\). The line slides but never changes its tilt — why is that?
- Find a slope where the x- and y-intercepts are the same point. What must \(b\) be? (Watch the dots merge at the origin.)
- Open scene 3 and give line B the same slope as line A but a different b. The readout should say parallel — confirm the lines never cross.
The Linear Function Lab
Two lines, two sliders each. Compare slopes, find intercepts, and connect the graph to a real fare.
Want to See This in 3D?
Optional, and always second. The lab above is where you measure and calculate; this is the same idea as an everyday object you can turn over and inspect. Open it when the lab already makes sense — or skip it entirely.
Where to Go Next
Back to the course, or deeper into the plan for Module 2.
Instructor: Dr. Goodluck Ijezie-Desbois, PharmD · Beta Academy · Room: TBA
This lab is built on the TEA Bluebonnet Learning — Secondary Mathematics open curriculum,
licensed CC BY-NC 4.0. Non-commercial classroom use.