Functions and graphs

A function is a machine: x in, y out. The linear function y = kx + b draws a line: k is the slope, b the y-intercept. Taxi price: y = 3·x + 10 — 10 € pickup plus 3 € per km. Reading the graph shows everything: where expensive, where cheap, where zero.

• ●y = 2x: line through zero, each step right = 2 up
• ●y = −x + 5: falling line, starts at 5
• ●k > 0 rises, k < 0 falls, k = 0 — flat