Maya bikes 4 miles every hour
Maya bikes at a steady speed. She travels four miles every hour. Let's plot her ride and read the story the graph tells.
The x-axis shows hours. The y-axis shows miles.
Our first point is at zero, zero — the origin.
What does zero, zero mean? At zero hours, Maya has biked zero miles. She hasn't started yet.
After one hour, she's biked four miles. That's the point one, four.
The point one, four is special. It tells us the unit rate: four miles per hour. We call this number k.
After two hours, she's biked eight miles. Plot two, eight.
After three hours, twelve miles. Plot three, twelve.
All these points line up — and the line goes straight through the origin. That's what makes it a proportional relationship.
Pick any point on the line. Three, twelve means: in three hours, Maya bikes twelve miles.
Every point follows the same rule: miles equals four times hours. So y equals four x.
Every point tells a story. The origin is the start, one comma k is the unit rate, and any x, y shows how far she's gone in that much time.