In this section we will focus on the meaning of slope as a rate of change, how to calculate slope, and how to convert rates of change into different units.
Horizontal and vertical lines have contextual meanings for their slope.
Objectives
When finished with this section, the student will be able to describe the meaning of slope as a rate of change with appropriate units of measure for a given context or graph.
When finished with this section, the student will be able to find the rate of change (slope) of a situation from its context, from a graph model, and from a table model.
When finished with this section, the student will be able to convert a rate of change into different units.
Slope is the measure of the steepness of a line. Here are a two ways to think about slope.
Definition:
The slope of the straight line through two points (x1, y1) and (x2, y2) is the ratio
where m stands for the slope.
Often this ratio is written as or where Δ means "change" as in Δy is "change in y".
Meaning:
Slope is a rate of change. How many miles per hour your are driving, how many dollars per hour you earn, how many cats per house are rates of change—slope!
To practice the basic measuring of slope, play with this flash animation.
Try selecting the same two points in different order.
The slope is the same, yet the calculations are slightly different.
Do you notice that there are negative slopes?
You will practice finding slope between two points as done in the flash activity above. Yet, to best understand slope you must dive into some problems where the numbers have meaning. So grab you thinking hats and get ready to dive into some investigations.
The following assignments and investigations are designed to help you better understand slope as a rate of change.
In the first assignment for this lesson you will be investigating two different situations.
In the first investigation you will look at how three characters save their money.
Looking at information shown in a table, you will consider slope as a rate of change.
In the second investigation you will look at some different options for flooring costs.
In this look into slope as a rate of change the information will be shown in a graph.
The slope of the straight line through two points (x1, y1) and (x2, y2) is the ratio
or 
where Δ means "change" as in Δy is "change in y". 
Slope is a rate of change. How many miles per hour your are driving, how many dollars per hour you earn, how many cats per house are rates of change—slope! 
In the second assignment for this lesson you will compare different speeds of cars in a race.