Because each input has an arrow to exactly one output in our mapping diagram, we can see that this is a function.
Now, we want to describe the relationship between the length of the rubber band and the force applied to it. Let's look at the mapping diagram again and note the changes in input and output of each step.
As each input increases by 0.7, the output increases by 2. This means that, for each increase in force by 0.7 Newtons, the length of the rubber band increases by 2 centimeters.
It seems like there is a straight line that would pass through all of our values. In other words, we should be able to find a linear equation that describes the relation between our inputs and outputs! To do this, we need to find two values.
We see that the line crosses the y-axis at (0,5). This means that the y-intercept is 5. Next, we will use two of the points to find the slope. Let's use ( 0.7, 7) and ( 0, 5).
Now we can write a linear equation in slope-intercept form that relates y to x.
y= 20/7x+ 5
The relationship between the length of the rubber band y and the force applied to it x can be described by the linear equation y= 207x+5.
