Functions
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Slope of a Line

Discover what makes a line steep — from hiking trails to y = mx + b

Imagine two hiking trails up the same mountain. Trail A is a gentle walk — it climbs 2 meters for every 8 meters forward. Trail B is a steep scramble — it climbs 6 meters over the same distance. You feel the difference in your legs, and that difference has a name in math: slope.

Slope measures steepness — how much a line rises (or falls) for each step to the right. It's written as rise ÷ run, and it shows up everywhere: the pitch of a roof, the grade of a road, the speed of a car, the rate of anything changing.

In this lesson, you'll build slope from scratch — measuring trails, drawing triangles, and discovering the equation y = mx + b — all on the graph with an AI tutor guiding you step by step.

Graph

FAQ

What is slope in math?
Slope measures how steep a line is. It's the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line: m = \frac{y_2 - y_1}{x_2 - x_1}. A bigger number means a steeper line.
How do I find the slope of a line from two points?
Use the slope formula: m = (y_2 - y_1) / (x_2 - x_1). Subtract the y-values (that's the rise) and divide by the difference in x-values (that's the run). For example, between (1, 2) and (4, 8): rise = 8 − 2 = 6, run = 4 − 1 = 3, so slope = 6/3 = 2.
What do positive and negative slopes mean?
A positive slope means the line goes uphill from left to right — like climbing a hill. A negative slope means it goes downhill. A slope of zero is a flat horizontal line. A vertical line has an undefined slope (you'd divide by zero).
What is slope-intercept form?
Slope-intercept form is y = mx + b, where m is the slope (steepness) and b is the y-intercept (where the line crosses the y-axis). It's the most common way to write a linear equation because you can read the slope and starting point directly from the equation.

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