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Mathematical Architects · Algebra I

Exploring Constant Change — Visual Lab

A constant rate of change draws a straight line. Move the sliders, watch the line rebuild itself, and see what slope really means.

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.

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The Linear Function Lab

Two lines, two sliders each. Compare slopes, find intercepts, and connect the graph to a real fare.

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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.
  • Turn on Line B (amber) to compare two slopes — the readout tells you which is steeper, or whether they're parallel.

Try this

  1. 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?
  2. Hold the slope fixed and drag b from \(-10\) to \(10\). The line slides but never changes its tilt — why is that?
  3. Find a slope where the x- and y-intercepts are the same point. What must \(b\) be? (Watch the dots merge at the origin.)
  4. Turn on Line B and give it the same slope as Line A but a different b. The readout should say parallel — confirm the lines never cross.
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Key Vocabulary & Standards

The five words that unlock Module 2, and the TEKS this lab is built to teach.

The vocabulary of a line
  • Slope  m The constant rate of change — how much \(y\) changes for each step of \(1\) in \(x\). Measured as \(\frac{\text{rise}}{\text{run}}\).
  • y-intercept  b The point \((0,\,b)\) where the line crosses the y-axis — the starting value of the situation.
  • x-intercept The point \((x,\,0)\) where the line crosses the x-axis — the input that makes \(y = 0\).
  • Slope-intercept form Writing a line as \(y = mx + b\), so the slope and starting value can be read straight off the equation.
  • Parallel lines Two lines with equal slopes. They rise at the same rate and never meet.
TEKS in this lab
A.2AA.2BA.2C A.3AA.3BA.3C A.4AA.4BA.4C

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.

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Where to Go Next

Back to the course, or deeper into the plan for Module 2.

Back to the Course

The full Algebra I itinerary — all five modules, worked examples, and the function grapher.

← Algebra I home

Course Syllabus

Policies, the studio learning environment, grading, and the full itinerary by grading period.

Read the Syllabus

Pacing Guide

Module 2 mapped to the Beta calendar — the 32 days of constant change, day by day.

View the Pacing Guide

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.