Linear Graphs — Slope and y-Intercept

A line has slope (rise/run) and y-intercept (where it crosses y). y = 2x + 1 goes up 2 for every 1 right, starting at y=1. Indirect aim: coordinate geometry, preparation for calculus, rate-of-change intuition.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Algebra
• Level: Ages 9-11

Objectives

• Graph linear equations y = mx + b
• Compute slope from two points
• Identify y-intercept
• Apply to real proportional data

Materials

• Graph paper
• Ruler
• Linear equation cards
• Real-world data (temperature over time)

Instructions

1. Graph y = 2x + 1: try x = 0,1,2; get y = 1,3,5. Plot. 2. Slope m = (y2-y1)/(x2-x1) = (3-1)/(1-0) = 2. 3. y-intercept b = 1 (where line crosses y-axis). 4. Graph y = -x + 3: slope -1, intercept 3. 5. Given two points (2,5) and (4,9): slope = 2, intercept = 1, so y = 2x+1. 6. Apply: temperature rising 2°/hour from 70°F at noon: T = 2h + 70. 7. Predict temp at 3pm: 76°. 8. File.

Educator tip

Slope is rate of change. Apply to real rates: speed, growth, income.

Assessment

Observe graphing accuracy, slope computation, and real application.

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• Data Collection and Analysis Project
• Algebra Word Problems
• Number Rods
• Sandpaper Numerals
• Spindle Boxes