There is a relationship, referred to as proportional, if two values exist in a constant ratio and rate of change. The slope of an equation can and will measure that rate of change. The worksheets presented here go over the topics of: rewriting given values as ordered pairs, plotting them on a graph with the correct axis labels, and drawing the resulting proportional slope. These worksheets demonstrate how to use the slope equation to find the slope of a line and chart that line on a graph. In addition, students will learn how to ask various questions related to proportional relationships.

# Print Proportional Relationships Worksheets

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Proportional Relationships and Slope Lesson

Learn how to use the slope equation to evaluate ratios and plot their relationship on a graph. In this lesson we are looking at the price of apples and how it stays constant with increases in volume.

## Proportional Relationships of Tables and Chairs

Based on the information given, use the numbers in the two ratios as two ordered pairs and plot them on the grid. You will analyze a series of graphs in this section. You will look at the number of chairs that comes with a differing number of tables.

## Practice the Skill

Based on the information given, answer the questions using the corresponding grids. You will look at 2 different scenarios. You will try to spot if a proportional relationship exists when traveling with a cycle and also the rate at which we read a book. There is a great deal that you can do to prove that this relationship exists or doesn't.

## Homework Worksheet

You will find four pieces of advice for students to work with to solve all the problems. On the homework sheet you will be looking to determine a relationship exists between the price of fuel and the cost of flour.

## Show the Skill Worksheet

Take a crack and see what you know so far. You will see if Dale eats nuts at a constant rate and if the number of squares and rectangles are found at the same proportions in two different settings.

## Warm Up

Time to get those synapses firing. You can use this worksheet to start your day off with this topic or to review it after you have already covered it. This will also help give you more practice with analyzing graphs.

## What are Proportional Relationships?

In the seventh grade, you may hear words like "inversely proportional" or "directly proportional," and you'll be left wondering what proportional even means. Proportional relationships are a vital part of education and are something you must familiarize yourself with.

This concept defines the relationship between two different variables. These can be variables of anything like price and amount or number of objects and length. In simple terms, it states how much one quantity is to another. Using our previous example, it could be price in relation to an amount.

When two variables are proportional to one another, it means that when one variable changes (increases or decreases), it directly affects the other variable. When two variables are in such a relation, they are connected to a constant multiplicatively.

In mathematics, this relationship forms a linear equation, such that one variable (x) is in proportion to another (y). It can be represented by the formula:

K = x/y

In this formula, k is the constant variable that connects the two variables x and y. k is also called the constant of proportionality.

For example, if an apple costs $1.30 a pound, the cost will also increase as the number of apples you buy increases. If we replace this statement with a formula, then:

Let the number of apples be x, and the cost be y.

y = kx

y = 1.30x

**Types pf Proportional Relationships**

They can be divided into two main types:

**1. Direct Proportional**: when one variable(x) increases, so does the other (y). And when one variable decreases, so does the other. y = kx

**2. Inverse Proportional**: when one variable (x) increases, the other variable (y) decreases, and vice versa. y = k/x

**On a Graph**

A proportional relationship graph between two variables plots the values of the two variables on the horizontal axis (called the x-axis) and the vertical axis (called the y-axis).

When two values are directly proportional, the resultant graph is a straight-line graph that passes through the origin. The resulting graph is curved when two values are inversely proportional to one another.

If the value of the proportionality (k) constant is positive, the graph has a positive gradient (moving upwards). If the value of the constant of proportionality (k) is negative, the graph has a negative gradient (moving downwards).

**How to Solve These Types of Problems:**

Let's consider the problem below where you need to find the missing value of y, given that x is directly proportional to y:

x |
1 | 4 | 8 |

y |
3 | ? | 24 |

Since to formula for direct proportion is y = kx, we need to find the value of the constant k. to do that, we can use the two known values of x and y. in this case, let's use x=1, y=3.

y = kx

3 = k (1)

k = 3

Since we now know the value of k, we can repeat the step with the unknown value.

y = kx

y = 3(4)

y = 12

in solving proportional relationship problems, you must first find the value of the constant (k) and then use it to solve for one of the variables. At the same time, the other is known using the correct formula.

**Conclusion**

Understanding this concept of what mathematical relationships are and how to solve them only brings you almost 70% of the way. For the other 30%, you need to practice. Think of it this way, the level of your mastery of proportional relationships is directly proportional to the amount of practice you do.