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Graphing Proportional Relationships

Grade 8 Math Worksheets

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other is constant.

Table of Contents:

  • Graphing Proportional Relationships
  • Solved Examples
  • FAQs

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Graphing Proportional Relationships - Grade 8 Math Worksheet PDF

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Graphing Proportional Relationships

Graphing proportional relationships involves plotting points on a coordinate plane and connecting them with a straight line.

Here’s how to do it:

1. Understand what proportional relationships are. A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other is constant. For example, if you have a recipe that calls for 2 cups of flour for every 1 cup of milk, this is a proportional relationship.

2. Determine the values for the two quantities. For example, if you’re graphing the proportional relationship between the number of hours worked and the amount earned, you’ll need to determine the values for both hours worked and amount earned.

3. Choose a scale for the axes. The scale should be large enough to fit all of the data points, but small enough to show the relationship clearly.

4. Plot the data points on the coordinate plane. Each data point represents a pair of values for the two quantities. For example, if you worked 2 hours and earned $20, you would plot the point (2, 20).

5. Connect the points with a straight line. The line should pass through all of the data points. If the relationship is proportional, the line should be straight and pass through the origin (0,0).

6. Label the axes with the units of measurement. For example, if you’re graphing the relationship between the number of hours worked and the amount earned, you would label the x-axis “Hours Worked” and the y-axis “Amount Earned ($)”.

By graphing proportional relationships, you can visualize the relationship between two quantities and see how they change together. This can be useful for understanding patterns and making predictions.

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Solved Examples 

If you travel 300 miles in 6 hours, how far can you travel in 8 hours?

To graph this proportional relationship, you would plot the point (6, 300) and then extend the line to find the point at 8 hours. However, without a diagram, you can use the proportional relationship to solve for the missing value. Since the ratio of distance to time is constant, we can write the equation:

distance/time = constant

 

Solving for the constant, we get:

300/6 = constant

constant = 50

 

Now we can use the constant to find the distance traveled in 8 hours:

distance/8 = 50

distance = 400 miles

 

Therefore, you can travel 400 miles in 8 hours.

 

If you can paint a room in 6 hours, how long will it take you to paint 3 rooms?

To graph this proportional relationship, you would plot the point (1, 6) and then extend the line to find the time for painting 3 rooms. However, without a diagram, you can use the proportional relationship to solve for the missing value. Since the ratio of rooms painted to time is constant, we can write the equation:

rooms/time = constant

 

Solving for the constant, we get:

1/6 = constant

constant = 1/6

 

Now we can use the constant to find the time to paint 3 rooms:

3/time = 1/6

time = 18 hours

 

Therefore, it will take 18 hours to paint 3 rooms.

 

If a car uses 5 gallons of gas to travel 100 miles, how many gallons of gas will it use to travel 250 miles?

To graph this proportional relationship, you would plot the point (100, 5) and then extend the line to find the point for 250 miles. However, without a diagram, you can use the proportional relationship to solve for the missing value. Since the ratio of gas used to distance traveled is constant, we can write the equation:

gas/distance = constant

 

Solving for the constant, we get:

5/100 = constant

constant = 0.05

 

Now we can use the constant to find the gas used to travel 250 miles:

gas/250 = 0.05

gas = 12.5 gallons

 

Therefore, the car will use 12.5 gallons of gas to travel 250 miles.

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FAQS

What is a proportional relationship?

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other is constant. For example, if the ratio of distance to time is constant, then the relationship between distance and time is proportional.

How do you graph a proportional relationship?

To graph a proportional relationship, you plot the data points on a coordinate plane and connect them with a straight line. The line should pass through all of the data points, and if the relationship is proportional, the line should be straight and pass through the origin (0,0).

What is the equation for a proportional relationship?

The equation for a proportional relationship is y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of proportionality.

How do you find the constant of proportionality?

To find the constant of proportionality, you can use the formula k = y/x, where k is the constant, y is the dependent variable, and x is the independent variable. The constant of proportionality represents the ratio of the dependent variable to the independent variable.

What are some real-world examples of proportional relationships?

Real-world examples of proportional relationships include distance traveled and time taken, speed and distance, cost and quantity, and weight and price.

How do you use graphing proportional relationships to make predictions?

By graphing proportional relationships, you can see the relationship between two quantities and use the line of best fit to make predictions. For example, if you know the distance traveled and the time taken, you can use the line of best fit to predict the time taken for a different distance traveled.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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