← Back to Math Adventures

Slope & Lines

Overview

Rise over Run.

What is it?

Understanding y = mx + b.

History

Descartes invented the coordinate plane while watching a fly on his ceiling.

Key Idea

m is the move (slope), b is the begin (y-intercept).

Practice This Topic

Concept Guide

Plain English: Every straight line can be described by two things: Where it starts (b) and how steep it is (m). Positive slope goes up hill, negative slope goes down hill.

Real-world example: Road grades (steepness), Roof pitches, Economy trends.

Common Pitfall

Mixing up x and y when calculating rise over run. Slope is Change in Y divided by Change in X.

Word Problem
"A plumber charges $100 to show up (b) and $50 per hour (m)."
Reasoning: Equation: y = 50x + 100. Slope is 50. Intercept is 100.

Practice Examples

Graphing
y = 2x + 1 Start at 1. Go Up 2, Right 1.
Plot points and connect.