Lesson 9: Slope & Linear Equations
Slope measures how steep a line is — the rate at which y changes as x increases. Combined with the y-intercept, slope gives us the slope-intercept form: y = mx + b, the most useful equation in all of middle school math.
Key Concepts
What Is Slope?
Slope = rise/run = (y₂ - y₁)/(x₂ - x₁). Positive slope: line goes up left-to-right. Negative: goes down. Zero slope: horizontal. Undefined slope: vertical (division by zero).
Slope-Intercept Form
y = mx + b. m = slope. b = y-intercept (where the line crosses the y-axis). y = 2x + 3: slope 2, y-intercept 3. To graph: start at (0,3), go up 2 and right 1 to find the next point.
Finding Slope from Two Points
Given (1, 3) and (4, 9): slope = (9-3)/(4-1) = 6/3 = 2. Always subtract in the same order — (y₂-y₁) and (x₂-x₁).
Standard Form
Ax + By = C. Useful for integer coefficients. To convert to slope-intercept: solve for y. 2x + 3y = 12 → 3y = -2x + 12 → y = -2/3 x + 4.
🔬 Interactive Lab: Slope & Linear Equations Lab
✅ Check Your Understanding
1. What is the slope of a line through (1,2) and (4,8)?
2. In y = -3x + 5, what is the y-intercept?
3. A horizontal line has a slope of: