Writing Slope-Intercept Form Equations
Year 9 Mathematics Understanding y = mx + b
What is Slope-Intercept Form?
The equation y = mx + b m represents the slope (rate of change) b represents the y-intercept (where line crosses y-axis) Most common form for writing linear equations
Quick Check: Identify the Parts
Look at this equation: y = 3x - 2 What is the slope (m)? What is the y-intercept (b)?
Method 1: Given Slope and Y-Intercept
Simplest case - direct substitution Example: slope = 2, y-intercept = 5 Substitute into y = mx + b Answer: y = 2x + 5
Practice: Slope and Y-Intercept Given
Try these examples: 1) slope = -3, y-intercept = 7 2) slope = 1/2, y-intercept = -4 3) slope = 0, y-intercept = 6
Method 2: Given Slope and One Point
Use point-slope form first: y - y₁ = m(x - x₁) Then rearrange to slope-intercept form Example: slope = 3, point (2, 8) y - 8 = 3(x - 2) → y = 3x + 2
Method 3: Given Two Points
Step 1: Calculate slope using m = (y₂ - y₁)/(x₂ - x₁) Step 2: Use slope and either point in point-slope form Step 3: Convert to slope-intercept form Example: points (1, 3) and (4, 9)
Challenge Problem
Find the equation of the line passing through: Point A: (-2, 5) Point B: (3, -10) Work with a partner and show all steps!
Key Takeaway
"Every linear relationship can be expressed as y = mx + b. The method you choose depends on what information you're given."
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