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Linear Functions: Slope & Y-Intercept

対象: High Schoolカテゴリ: Math

説明

This animation introduces linear functions of the form y = mx + b by visually demonstrating how the slope (m) and y-intercept (b) affect the graph. A line rotates as the slope changes from -2 to 2, then shifts vertically as the intercept changes from -3 to 3. A rise/run right-triangle indicator reinforces the geometric meaning of slope.

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Linear Functions: Slope & Y-Intercept

Description

This animation introduces linear functions of the form y = mx + b by visually demonstrating how the slope (m) and y-intercept (b) affect the graph. A line rotates as the slope changes from -2 to 2, then shifts vertically as the intercept changes from -3 to 3. A rise/run right-triangle indicator reinforces the geometric meaning of slope.

Phases

# Phase Name Duration Description
1 Introduction 5s Display axes and the formula y = mx + b; draw the initial line at m=1, b=0
2 Slope Animation 15s Animate m from -2 to 2, line rotates; show rise/run triangle updating live
3 Intercept Animation 12s Animate b from -3 to 3, line shifts up and down; b label highlights
4 Summary 8s Settle at m=1, b=1; label all parts; fade out with key takeaway text

Layout

+-----------------------------------------------+
|  y = mx + b                   [formula top]   |
|                                                |
|        ^                                       |
|        |       /  <- line                      |
|        |      /                                |
|  ------+-----/-------->                        |
|        |    /  [rise/run triangle]             |
|        |   /                                   |
|                                                |
|  m = 1.00   b = 0.00         [value labels]   |
+-----------------------------------------------+

Area Descriptions

Area Content Notes
Center Axes + plotted line NumberPlane-style axes via Axes
Top center MathTex formula y = mx + b Updates color highlights as params change
Bottom left m and b value readouts Decimal displays driven by ValueTrackers
On graph Rise/run right triangle Drawn near x=1 to show slope visually

Assets & Dependencies

  • Fonts: LaTeX
  • Colors: LINE_COLOR = YELLOW, SLOPE_COLOR = GREEN, INTERCEPT_COLOR = BLUE, TRIANGLE_COLOR = ORANGE, BG = #1a1a2e
  • Manim version: ManimCE 0.19.1

Notes

  • ValueTracker for m and b; use always_redraw for the line and triangle
  • Rise/run triangle anchored to a fixed x-window so it stays on screen during rotation
  • Keep axes range x: [-5, 5], y: [-5, 5]