How do I do the write an equation one?

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Modeling with tables, equations, and graphs

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

. Each topping costs

$ 2

Representing with a table

We know that the cost of a pizza with

0

toppings is

$ 6

, the cost of a pizza with

1

topping is

$ 2

more which is

$ 8

, and so on. Here's a table showing this:

Toppings on the pizza $(x)$ ‍	Total cost $(y)$ ‍
$0$ ‍	$$ 6$ ‍
$1$ ‍	$$ 8$ ‍
$2$ ‍	$$ 10$ ‍
$3$ ‍	$$ 12$ ‍
$4$ ‍	$$ 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

7

toppings on the pizza. (Other than that it'd be gross!)

Let's see how this table makes sense for a small pizza with

4

toppings.

Here's the cost of just the pizza:

$$ 6$ ‍

Here's the cost of the

4

toppings:

$4$ ‍ toppings $\cdot$ ‍ $$ 2$ ‍ per topping $=$ ‍ $$ 8$ ‍

This leads to the total cost of

$$ 6 + $ 8 = $ 14$ ‍.

How much would a small pizza with $5$ ‍ toppings cost?

$

[I need help! Please show me the solution.]

Representing with an equation

Let's write an equation for the total cost

y

of a pizza with

x

toppings.

Here's the cost of just the pizza:

$$ 6$ ‍

Here's the cost of

x

toppings:

$x$ ‍ toppings $\cdot$ ‍ $$ 2$ ‍ per topping $=$ ‍ $x \cdot 2 = 2 x$ ‍

So here's the equation for the total cost

y

of a small pizza:

$y = 6 + 2 x$ ‍

Let's see how this makes sense for a small pizza with

3

toppings:

$x = 3$ ‍ because there are $3$ ‍ toppings

The total cost is $6 + 2 (3) = 6 + 6 = $ 12$ ‍

Use the equation to find the cost of a small pizza with $100$ ‍ toppings.

$

[I need help! Please show me the solution.]

Representing with a graph

We can create ordered pairs from the

x

and

y

values:

Toppings on the pizza $(x)$ ‍	Total cost $(y)$ ‍	Ordered pair $(x, y)$ ‍
$0$ ‍	$$ 6$ ‍	$(0, 6)$ ‍
$1$ ‍	$$ 8$ ‍	$(1, 8)$ ‍
$2$ ‍	$$ 10$ ‍	$(2, 10)$ ‍
$3$ ‍	$$ 12$ ‍	$(3, 12)$ ‍
$4$ ‍	$$ 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

, and each topping costs

$ 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

2

scoops of ice cream for

$ 3

. Each additional scoop costs

$ 1

Complete the table to represent the relationship.

Scoops of ice cream $(x)$ ‍	Total cost $(y)$ ‍
$2$ ‍	$$ 3$ ‍
$3$ ‍	$ Your answer should be an integer, like $6$ ‍ a simplified proper fraction, like $3 / 5$ ‍ a simplified improper fraction, like $7 / 4$ ‍ a mixed number, like $1 3 / 4$ ‍ an exact decimal, like $0.75$ ‍ a multiple of pi, like $12 pi$ ‍ or $2 / 3 pi$ ‍
$4$ ‍	$ Your answer should be an integer, like $6$ ‍ a simplified proper fraction, like $3 / 5$ ‍ a simplified improper fraction, like $7 / 4$ ‍ a mixed number, like $1 3 / 4$ ‍ an exact decimal, like $0.75$ ‍ a multiple of pi, like $12 pi$ ‍ or $2 / 3 pi$ ‍
$5$ ‍	$ Your answer should be an integer, like $6$ ‍ a simplified proper fraction, like $3 / 5$ ‍ a simplified improper fraction, like $7 / 4$ ‍ a mixed number, like $1 3 / 4$ ‍ an exact decimal, like $0.75$ ‍ a multiple of pi, like $12 pi$ ‍ or $2 / 3 pi$ ‍
$6$ ‍	$ Your answer should be an integer, like $6$ ‍ a simplified proper fraction, like $3 / 5$ ‍ a simplified improper fraction, like $7 / 4$ ‍ a mixed number, like $1 3 / 4$ ‍ an exact decimal, like $0.75$ ‍ a multiple of pi, like $12 pi$ ‍ or $2 / 3 pi$ ‍

[Show solution]

Write an equation to represent the relationship.
Remember to use $x$ ‍ for scoops of ice cream and $y$ ‍ for total cost.

[Show solution]

Plot the points from the table on the graph to represent the relationship.
Be sure to plot the exact points in the table above!

[Show solution]

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!

Want to join the conversation?

Sort by:

Yanal Atallah
Posted 4 years ago. Direct link to Yanal Atallah's post “Hello! I hope you are hav...”
Hello! I hope you are having a great day. I think that the advantages are that they can show a lot of information that is easily understood. Even the Table in functions can be easy to use and practical and you will find a lot of solutions for just one equation. Equations are also easier to find with small numbers and they also show the relationship between the x-axis and the y-axis. The disadvantages of Equations are that with big numbers, the answer will be weird. A Disadvantage of using the Table is that when you use decimals, the Table won't work. The Disadvantage of using a graph is that you can probably have two unpredictable variables. For me, I prefer using the table more than the graph and the equation. I think it is easier for me because I can double-check my answer with each number in the table. Thanks!
Button navigates to signup pageComment on Yanal Atallah's post “Hello! I hope you are hav...”
(31 votes)
Answer
Emilynn
Posted a year ago. Direct link to Emilynn's post “I would argue that a 7-to...”
I would argue that a 7-topping pizza is, indeed, not "gross". For example, the Costco Food Court combination pizza (which was discontinued in 2020) had six toppings on top of cheese. It was considered 'good pizza', based on all the positive reviews it received, as well as the despair people shared when Costco stopped selling it.
Another example is the supreme pizza at Papa Johns. This pizza also contains 6 toppings, and yet people still buy and enjoy it. Not to mention other chains, such as Pizza Hut, allow you to put up to 7 toppings on your pizza.
It really comes down to personal preference, but needless to say, I personally think that just because your pizza has 7+ toppings, doesn't mean that it's "gross".
Button navigates to signup pageComment on Emilynn's post “I would argue that a 7-to...”
(15 votes)
Answer
- 3327044
  Posted 11 days ago. Direct link to 3327044's post “Meat lovers is also a gre...”
  Meat lovers is also a great example to this, depending what types of meat and how many options are available!
  Button navigates to signup page
  (1 vote)
bdouglas
Posted 4 years ago. Direct link to bdouglas's post “I think the Graph is easi...”
I think the Graph is easier, these questions were so easy it was hard to figure it out, I thought it was gonna be hard.
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(8 votes)
Answer
Elizabeth
Posted 6 years ago. Direct link to Elizabeth's post “Is there an easier way to...”
Is there an easier way to learn how to read and write the xy equations?
Button navigates to signup pageComment on Elizabeth's post “Is there an easier way to...”
(8 votes)
Answer
- 2700032
  Posted 11 days ago. Direct link to 2700032's post “Imo, it's the most simple...”
  Imo, it's the most simple way, but that's just me.
  Button navigates to signup page
  (1 vote)
saintleonacademy
Posted 4 months ago. Direct link to saintleonacademy's post “For any people having tro...”
For any people having trouble with the ice cream scoop equation, I have a simple explanation.

Because the base cost of a cone with no scoops is one dollar, (0,1) The equation has a plus-one.( y = x + 1 )

It's just like the base pizza price equation which is 6$ for a pizza with no toppings, (0,6) And each topping costs two dollars. so you are multiplying the amount of toppings by 2, and then you add the base price which is six. Therefore, the equation is, ( y = 2x + 6 )
Button navigates to signup pageComment on saintleonacademy's post “For any people having tro...”
(7 votes)
Answer
Ali Abbasabadi
Posted 7 months ago. Direct link to Ali Abbasabadi's post “Graphs are pictures that ...”
Graphs are pictures that show how data changes or relates to each other. They are good for showing the big picture of your data, like how it goes up or down over time, or how it compares to other data. Graphs can also help you find patterns or unusual points in your data.
Tables are lists that show the exact values of your data. They are good for looking up specific numbers or comparing two numbers. Tables can also show different kinds of information in one place, like names, dates, and amounts.
Equations are formulas that show how variables affect each other mathematically. They are good for finding out what happens when you change one variable or another. Equations can also tell you the exact relationship between variables, while graphs can only show you an estimate.
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(7 votes)
Answer
Sanchez, Susana
Posted 3 years ago. Direct link to Sanchez, Susana's post “i think that the advantag...”
i think that the advantage is that if u know how to do works from a graph than it will be really easy to put it in the plotting graph and the disadvantage is like when you have to find a missing number, but if you get it wrong then thats when the bigger problem begins.
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(5 votes)
Answer
Breceda, Adrian
Posted 4 years ago. Direct link to Breceda, Adrian's post “How do I do the write an ...”
How do I do the write an equation one?
Button navigates to signup pageComment on Breceda, Adrian's post “How do I do the write an ...”
(1 vote)
Answer
- chloe.lawson.26
  Posted 4 years ago. Direct link to chloe.lawson.26's post “Just look for a patteren ...”
  Just look for a patteren and you will get it! Good luck
  Comment on chloe.lawson.26's post “Just look for a patteren ...”
  (5 votes)
Salgado, Miguel
Posted 3 years ago. Direct link to Salgado, Miguel's post “Basically if you have two...”
Basically if you have two variables and no exponents, then you are dealing with a linear equations. Exponents would signify that you are dealing with some sort of curve, possibly a parabola in the case of a quadratic. Also if you have just a single variable and still no exponents and are being asked to graph it as a line on a two dimensional grid, then you are dealing with a vertical or horizontal line. For instance x = 1 is a vertical line that crosses x at 1. While y = 2 is a horizontal line that crosses y at 2.
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(3 votes)
Answer
John Trainor
Posted 4 months ago. Direct link to John Trainor's post “An equation is very valua...”
An equation is very valuable for calculating large values.
A table is good for listing a small number of distinct values.
A graph is valuable for getting the general idea of the relationship between the independent and dependent variables.
Button navigates to signup pageComment on John Trainor's post “An equation is very valua...”
(3 votes)
Answer

8th grade

Course: 8th grade > Unit 3

Modeling with tables, equations, and graphs

Representing with a table

Representing with an equation

Representing with a graph

We did it!

Give it a try!

Comparing the three different ways

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