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# Algebra 1 Inverse Variation

## Direct Variation Answers

❶The going is very slow, because your friend on his terrible old bike can only average about 10 miles an hour.

If we translate the definition into the language of mathematics, we get an equation that looks like this:. Get access risk-free for 30 days, just create an account. Seeing this concept in a more visual form, instead of equations and tables, might help you understand the concept better. Take a look at what the graph of an inverse variation looks like:. What jumps out at me from the graph is that curvy thing that is definitely not a line.

Linear relationships and inverse variations are very different animals! There are lots of other real-life examples of inverse variations. How quickly a glass of cold water cools down on a warm day varies inversely with the temperature. The force required to break a board varies inversely with how long it is. Where musicians place their fingers on a stringed instrument is determined by the inverse variation between string length and vibration frequency.

When the product of two variables is constant they are said to have inverse variation. In equation form it looks like this:. When one variable is very large, the other is very small, and also the other way around. Examples of inverse variation can be found in stringed instruments, warming water, and bike rides, just to name a few.

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Solving Equations of Inverse Variation. Direct and Inverse Variation Problems: Solving Equations of Direct Variation. How to Define a Zero and Negative Exponent. Definition, Properties, and Proof Theorems. Simplifying Expressions with Rational Exponents. What is a Radical Function? Critical Thinking Math Problems: High School Algebra II: Holt McDougal Larson Geometry: Holt McDougal Algebra 2: Have you heard of an inverse variation?

This is my bike. The equation for this scenario is: Definition This bike riding scenario represents an inverse variation. Equations, Tables, Graphs If we translate the definition into the language of mathematics, we get an equation that looks like this: Try it risk-free No obligation, cancel anytime. Want to learn more? Select a subject to preview related courses: We can then make a table for each value of k we choose: Take a look at what the graph of an inverse variation looks like: Other Life Examples There are lots of other real-life examples of inverse variations.

Lesson Summary When the product of two variables is constant they are said to have inverse variation. In equation form it looks like this: Unlock Your Education See for yourself why 30 million people use Study.

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Browse Articles By Category Browse an area of study or degree level. You are viewing lesson Lesson 23 in chapter 8 of the course:. Help and Review 25 chapters lessons. High School Algebra - Basic High School Algebra - Solving Math High School Algebra - Decimals and High School Algebra - Percent High School Algebra - Real Numbers High School Algebra - Exponential High School Algebra - Radical Algebraic Equations and Expressions: A person with a mental age of 25 and a chronological age of 20 has an IQ of What is the chronological age of a person with a mental age of 40 and an IQ of 80?

Heart rates and life spans of most mammals can be modeled using inverse variation. The bar graph shows the average heart rate and the average life span of five mammals. You will use the data to solve. Use the data shown for cats at the bottom of the previous page to write the equation that models this relationship. Is the inverse variation equation in part a an exact model or an approximate model for the data shown for squirrels?

Mice have an average heart rate of beats per minute. Determine their average life span, rounded to the nearest year. Use the data shown for horses to write the equation that models this relationship.

Is the inverse variation equation in part a an exact model or an approximate model for the data shown for lions?

Elephants have an average heart rate of 27 beats per minute. Determine their average life span. Since IQ varies directly with mental age m and inversely with chronological age c. Introductory and Intermediate Algebra for College Students.

## Main Topics

Overview Direct and inverse variation refer to relationships between variables, so that when one variable changes the other variable changes by a specified amount. Both direct and inverse variation can be applied in many different ways. Figure 1: Definitions of direct and inverse variation.

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Inverse variation means that as one variable increases, the other variable decreases. In equations of inverse variation, the product of the two variables is a constant. Suppose when x equals 3, y equals 20; when x equals 6, y equals 10; and when x equals 12, y equals 5.