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What Is the Slope of a Line?(With Examples)

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.

Grade 8Key Stage 3-4Årskurs 8-9Klasse 8

📖Definition

📐Formula

m = (y₂ - y₁) / (x₂ - x₁) = rise / run

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.

m = (y₂ - y₁) / (x₂ - x₁)

⚠️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

Easy

Find the slope between (1, 2) and (3, 6)

Answer: m = 2

Medium

Find the slope between (-2, 5) and (4, -1)

Answer: m = -1

Hard

A line passes through (3, -2) and has slope 2/3. Find y when x = 9.

Answer: y = 2

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Worked Examples

Slope Example: Finding Slope Between Two Pointsmedium

Linear Equations Coordinate Plane Graphing Lines Parallel and Perpendicular Lines

Curriculum Alignment

CommonCore (8.EE.B.6)KS3KMK

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