Linear Functions — Cheat sheet

Key method

For distinct inputs,

Positive $m$ means increasing, negative $m$ decreasing, and zero $m$ constant. A vertical line is not the graph of a function $y=f(x)$.

Example

A line through $(1,3)$ and $(4,9)$ has slope $(9-3)/(4-1)=2$. Substituting $(1,3)$ into $y=2x+b$ gives $b=1$. Hence $f(x)=2x+1$ and increasing $x$ by $0.5$ increases the output by $1$.

Avoid this mistake

The intercept is the output at $x=0$, not the input at which the graph crosses the horizontal axis.