Math 1 · Unit 3 · Lesson 1
Slope: The Rate of Change Gets Its Name
The average rate of change from Unit 2 is the same on every stretch of a straight line, so it gets a name: slope, the rise over the run. The top is the rise, how much y went up or down. The bottom is the run, how far you went to the right. Find it from a graph, a table, or two points, then read the sign and the size.
The big idea
Slope is the rate of change with a name. It is the fraction rise over run: the change in y on top, the change in x on the bottom, how much the line goes up or down for each step to the right. A straight line has the same slope everywhere, so any two points give it: count the staircase on a graph, read the constant change in a table, or subtract two points in the same order. Then read the number. Positive climbs, negative falls, zero is a flat line, a vertical line has no slope at all, and a bigger size means steeper. Next lesson this number takes its seat in the form every line shares.
The parts of this lesson
Each part is its own short page. Go in order, or pick the one you need.
Printables
One page with the fraction, the three ways to find slope, the sign and size rules, and a worked example. Plus a worksheet with grids and an answer key, and a short lesson plan.