See how relationships between two variables like number of toppings and cost of pizza can be represented using a table, equation, or a graph.
Math is all about relationships. For example, how can we describe the relationship between a person's height and weight? Or how can we describe the relationship between how much money you make and how many hours you work?
The three main ways to represent a relationship in math are using a table, a graph, or an equation. In this article, we'll represent the same relationship with a table, graph, and equation to see how this works.
Example relationship: A pizza company sells a small pizza for $6\$6 . Each topping costs $2\$2.

Representing with a table

We know that the cost of a pizza with 00 toppings is $6\$6, the cost of a pizza with 11 topping is $2\$2 more which is $8\$8, and so on. Here's a table showing this:
Toppings on the pizza (x)(x)Total cost (y)(y)
00$6\$6
11$8\$8
22$10\$10
33$12\$12
44$14\$14
Of course, this table just shows the total cost for a few of the possible number of toppings. For example, there's no reason we couldn't have 77 toppings on the pizza. (Other than that it'd be gross!)
Let's see how this table makes sense for a small pizza with 44 toppings.
Here's the cost of just the pizza:
$6\$\greenD6
Here's the cost of the 4\blueD4 toppings:
4\blueD4 toppings \cdot $2\$2 per topping = = $8\$\goldD8
This leads to the total cost of
$6+$8=$14\$\greenD6 + \$\goldD8 = \$14.
How much would a small pizza with 55 toppings cost?
$\$
Let's extend the table one more row:
Toppings on the pizza (x)(x)Total cost (y)(y)
00$6\$6
11$8\$8
22$10\$10
33$12\$12
44$14\$14
55$16\$16
A small pizza with 55 toppings costs $16\$16.

Representing with an equation

Let's write an equation for the total cost yy of a pizza with xx toppings.
Here's the cost of just the pizza:
$6\$\greenD6
Here's the cost of xx toppings:
xx toppings \cdot $2\$2 per topping = = x2=2xx \cdot 2 = \goldD{2x}
So here's the equation for the total cost yy of a small pizza:
y=6+2xy = \greenD6 + \goldD{2x}
Let's see how this makes sense for a small pizza with 33 toppings:
x=3x = \blueD3 because there are 3\blueD3 toppings
The total cost is 6+2(3)=6+6=$126 + 2(\blueD3) = 6 + 6 = \$12
Use the equation to find the cost of a small pizza with 100100 toppings.
$\$
x=100x = \blueD{100} because there are 100\blueD{100} toppings
The total cost is 6+2(100)=6+200=$2066 + 2(\blueD{100}) = 6 + 200 = \$206

Representing with a graph

We can create ordered pairs from the xx and yy values:
Toppings on the pizza (x)(x)Total cost (y)(y)Ordered pair (x,y)(x , y)
00$6\$6(0,6)(0, 6)
11$8\$8(1,8)(1, 8)
22$10\$10(2,10)(2, 10)
33$12\$12(3,12)(3, 12)
44$14\$14(4,14)(4, 14)
We can use these ordered pairs to create a graph:

Cool! Notice how the graph helps us easily see that the total cost of the small pizza increases as we add more toppings.

We did it!

We represented the situation where a pizza company sells a small pizza for $6\$6, and each topping costs $2\$2 using a table, an equation, and a graph.
What's really cool is we used these three methods to represent the same relationship. The table allowed us to see exactly how much a pizza with different number of toppings costs, the equation gave us a way to find the cost of a pizza with any number of toppings, and the graph helped us visually see the relationship.
Now let's give you a chance to create a table, an equation, and a graph to represent a relationship.

Give it a try!

An ice cream shop sells 22 scoops of ice cream for $3\$3. Each additional scoop costs $1\$1.
Complete the table to represent the relationship.
Scoops of ice cream (x)(x)Total cost (y)(y)
22$3\$3
33$
44$
55$
66$
Remember that each addition scoop adds $1\$1 to the total cost:
Scoops of ice cream (x)(x)Total cost (y)(y)
22$3\$3
33$4\$4
44$5\$5
55$6\$6
66$7\$7
Write an equation to represent the relationship.
Remember to use xx for scoops of ice cream and yy for total cost.
This equation is tricky!
We know that the cost of each addition scoop after 22 scoops is $1\$\blueD 1. So, the equation has to include
1x\blueD1 \cdot x.
In order for the equation to be true for the values x=2x =2 and y=3y=3 for example, we need to add 1\greenD 1. So, here's the equation:
y=1x+1y = \blueD1 \cdot x + \greenD1
We can also write it like this:
y=x+1y = x + \greenD 1
Plot the points from the table on the graph to represent the relationship.
Be sure to plot the exact points in the table above!
Here are the ordered pairs from the xx and yy values:
Scoops of ice cream (x)(x)Total cost (y)(y)Ordered pair (x,y)(x , y)
22$3\$3(2,3)(2, 3)
33$4\$4(3,4)(3, 4)
44$5\$5(4,5)(4, 5)
55$6\$6(5,6)(5, 6)
66$7\$7(6,7)(6, 7)
Here is the graph:

Comparing the three different ways

We learned that the three main ways to represent a relationship is with a table, an equation, or a graph.
What do you think are the advantages and disadvantages of each representation?
For example, why might someone use a graph instead of a table? Why might someone use an equation instead of a graph?
Feel free to discuss in the comments below!