So,
If we analyze the table of plastic chairs, we can notice that there's an addition of 4 between each term. That means that it is a linear function whose slope is given by the following:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{4}{4}=1[/tex]The triangle that you see means the change between each x and y terms, respectively.
The equation that satisfies this table is:
[tex]y=x+5[/tex]In the table of Wooden chairs, there's a multiplicative relationship. Where the ratio is:
[tex]\frac{22}{8}=\frac{33}{12}=\frac{44}{16}=2.75[/tex]So, the equation that represents this table is:
[tex]y=2.75x[/tex]A verbal description of the plastic chairs, could be that:
"The total rental cost has an initial cost of $5, which means that 5 chairs had been already rented. Each chair's rent cost $1, so that's y = x + 5 which is the total rental cost".
A verbal description of the wooden chairs, could be that:
"Each chair is rented with a price of 2.75$ per chair. So that's the total rental cost".
Comparing, the first table is not a directly proportional relationship because the line doesn't pass through the origin. The second one is actually a directly proportional relationship since it is a line that passes through the origin.