📖Definition
Slope measures the steepness and direction of a line. It tells you how much the line rises (or falls) for each unit it moves horizontally. Slope is often described as "rise over run" - the vertical change divided by the horizontal change.
📐Formula
To find slope between two points (x₁, y₁) and (x₂, y₂): subtract the y-values (rise) and divide by the difference in x-values (run). In y = mx + b, m is the slope.
📝Step-by-Step Guide
Identify Two Points
Find two points on the line with coordinates (x₁, y₁) and (x₂, y₂).
Calculate Rise
Subtract the y-coordinates: rise = y₂ - y₁.
Calculate Run
Subtract the x-coordinates: run = x₂ - x₁.
Divide Rise by Run
Slope = rise ÷ run. Simplify if possible.
⚠️Common Mistakes to Avoid
- Subtracting in different orders (y₂-y₁ but x₁-x₂)
- Confusing rise and run
- Dividing run by rise instead of rise by run
- Forgetting that vertical lines have undefined slope
- Thinking horizontal lines have undefined slope (they have slope 0)
✏️Practice Problems
Find the slope between (1, 2) and (3, 6)
Answer: m = 2
Find the slope between (-2, 5) and (4, -1)
Answer: m = -1
A line passes through (3, -2) and has slope 2/3. Find y when x = 9.
Answer: y = 2
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