We've looked at the slope as a rate of change. A rate compares two variables. So the slope can also be viewed as the relationship between two variables. We use the two variables "x" and "y". Why? because those are the two variables placed on the graph.
In a line the independent variable "x" and the dependent variable "y" are related. To
review the definition of these two variables click here.
To understand how these two variables are related think about a line on a graph and walking up or down the line like you would walk up or down a flight of stairs. Each time you take a step you "rise" a little and you go forward or "run" a little. The slope is how "steep" that line is. You could think of this as how much your foot rose over how much it ran or
m = rise / run.
How much I'm rising is the difference in the "y" values and how much I'm running is the difference in the "x" values. Let's think about this with stairs. If I simply walk up the stairs, I'm rising 1 foot and running 1 foot. So the slope is 1/1. But what if I change my staircase so that I rise 2 steps and run 1. Then my slope is 2/1 which is steeper than 1/1. If we think of our staircase and the slope of it as the steepness then we will see that the slope of 2, the greater number, is "steeper" than the staircase with the slope of 1, the smaller number.
Now, let's use this idea to gather even more information about how the slope can be found from tables. Think about our staircase where we stepped up 2 feet and then over 1 foot. If we took two steps we would go up four feet and over 2 feet. We can place this information in a table. ??????????? We can see that when "y" goes up two "x" goes up one. That is the relationship between "x" and "y".
Now you can practice finding the slope when given a table since you understand the relationship between the two variables.
We've looked at the slope as a rate of change. A rate compares two variables. So the slope can also be viewed as the relationship between two variables. We use the two variables "x" and "y". Why? because those are the two variables placed on the graph.
In a line the independent variable "x" and the dependent variable "y" are related. To
review the definition of these two variables click here.
To understand how these two variables are related think about a line on a graph and walking up or down the line like you would walk up or down a flight of stairs. Each time you take a step you "rise" a little and you go forward or "run" a little. The slope is how "steep" that line is. You could think of this as how much your foot rose over how much it ran or
m = rise / run.
How much I'm rising is the difference in the "y" values and how much I'm running is the difference in the "x" values. Let's think about this with stairs. If I simply walk up the stairs, I'm rising 1 foot and running 1 foot. So the slope is 1/1. But what if I change my staircase so that I rise 2 steps and run 1. Then my slope is 2/1 which is steeper than 1/1. If we think of our staircase and the slope of it as the steepness then we will see that the slope of 2, the greater number, is "steeper" than the staircase with the slope of 1, the smaller number.
Now, let's use this idea to gather even more information about how the slope can be found from tables. Think about our staircase where we stepped up 2 feet and then over 1 foot. If we took two steps we would go up four feet and over 2 feet. We can place this information in a table. ??????????? We can see that when "y" goes up two "x" goes up one. That is the relationship between "x" and "y".
Now you can practice finding the slope when given a table since you understand the relationship between the two variables.