Math 1 · Unit 3 · Lesson 1 · part 2 of 6
The rate of change gets its name
Unit 2 ended with the average rate of change: the change in the output over the change in the input, how...
The rate of change gets its name
Unit 2 ended with the average rate of change: the change in the output over the change in the input, how much y goes up or down for each step x takes to the right. For a straight line that number is the same on every interval (that is what made it straight in the connect-the-dots lesson). So it gets a name of its own: slope.
It is a fraction, the same fraction as before. The top (the numerator) is the rise: how much the output went up or down. The bottom (the denominator) is the run: how far you moved to the right. Simplify it like any fraction: a rise of 6 over a run of 4 is 64 = 32, which reads as up 3 for every 2 to the right.
You can find it three ways, and all three are the same fraction: from a graph (count the rise and the run between two points), from a table (the output changes by the same amount each step), and from two points (subtract the y values, subtract the x values, divide).