We will make a table where the independent variable is the side length of a square and the dependent variable is the perimeter. To do so, let's start by recalling the perimeter of a square.
P=4l
Here, l is the side length of the square. Now, we can evaluate this formula for several values of l.
l
P=4l
P
0
P=4( 0)
0
2
P=4( 2)
8
4
P=4( 4)
16
6
P=4( 6)
24
These points lie on a line. Consider that the value of l indicates the value of x and its corresponding value of P represents the value of y. These values form a ordered pair that can be plotted in a coordinate plane. Let's plot the ordered pairs and draw a line through the points.
Now, we can recall the formula for the area of a square.
A=l^2
Let's evaluate this formula for several values of l and construct a table with the results.
l
A=l^2
A
0
A=( 0)^2
0
2
A=( 2)^2
4
4
A=( 4)^2
16
6
A=( 6)^2
36
In this case, consider that the value of l indicates the value of x and its corresponding value of A represents the value of y. Let's plot the ordered pairs and draw a curve through the points.
Now, we can plot the obtained curves in the same coordinate plane.
Notice that the graph of the perimeter is a line, but the graph of the area is a curve. This means that the perimeter is a linear function of the side of the square and the area is a non-linear function of the side lenght.
