Linear Functions & Rate of Change

A linear function changes at a constant rate — its slope. The same idea, the average rate of change $\dfrac{f(b) - f(a)}{b - a}$, measures how fast any function climbs over an interval. The big skills:

• Compute a rate of change / slope from two points, a table, or a graph.
• Interpret slope and intercept in context — what the numbers mean (e.g. dollars per month, and the starting amount).
• Write the equation of a line from a slope and a point, or from two points.

These are real, released Regents questions; read what each number represents, not just its value.