Mathematics
Grade 11
15 min
Write and solve inverse variation equations
Write and solve inverse variation equations
What you'll learn
- Solve for the missing number (variable) in addition and subtraction problems with one-digit numbers, and show your work.
- Identify the missing number (variable) in an addition or subtraction equation with a box or letter representing the unknown.
- Explain how to find the missing number (variable) in an addition or subtraction problem using inverse operations in your own words.
- Solve for the missing number (variable) in addition and subtraction problems with two-digit numbers, and check your answer.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify an inverse variation relationship from a problem description or a set of data.
Write the general equation for an inverse variation relationship.
Calculate the constant of variation, k, given a corresponding pair of values.
Formulate the specific inverse variation equation for a given scenario.
Use an inverse variation equation to find an unknown value.
Model and solve real-world problems involving inverse variation.
Ever noticed that the more people who share a pizza, the smaller each person's slice gets? 🍕🤔 This is a perfect example of inverse variation in action!
This tutorial will guide you through the process of writing and solving inverse variation equations. You will learn how to model relationships where one quantity increases as a...
2
Key Concepts & Vocabulary
TermDefinitionExample
Inverse VariationA relationship between two variables in which the product is a constant. When one variable increases, the other variable decreases proportionally.If y varies inversely as x, it means as x doubles, y is halved.
Constant of Variation (k)The non-zero constant value that represents the product of the two variables in an inverse variation relationship. It is often denoted by the letter 'k'.In the equation y = 12/x, the constant of variation is 12.
General Equation of Inverse VariationThe formula that describes any inverse variation relationship before the specific constant is known.The general equation is y = k/x, where k is the constant of variation.
Specific Equation of Inverse VariationThe equation that describes a particular inverse variatio...
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Core Formulas
General Inverse Variation Equation
y = \frac{k}{x}
Use this formula to represent the relationship that 'y varies inversely as x' or 'y is inversely proportional to x'. Here, k is the constant of variation and k ≠ 0.
Formula for the Constant of Variation
k = xy
To find the constant of variation (k), multiply any given pair of corresponding x and y values.
Proportion Form for Solving
x_1 y_1 = x_2 y_2
This is a powerful shortcut for solving inverse variation problems. If you know one pair of values (x₁, y₁) and half of another pair (e.g., x₂), you can solve for the missing value (y₂) without first explicitly finding k.
4 more steps in this tutorial
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Challenging
The electrical resistance (R) of a wire of a certain length is inversely proportional to the square of its diameter (d). If a wire with a diameter of 2 mm has a resistance of 45 ohms, what is the resistance of a wire of the same material and length with a diameter of 3 mm?
A.20 ohms
B.30 ohms
C.67.5 ohms
D.101.25 ohms
Challenging
The variable y varies inversely with the expression (x + 5). If y = 8 when x = 3, what is the value of x when y = 4?
A.16
B.6
C.11
D.1
Challenging
A graph of an inverse variation function y = k/x passes through the points (a, 24) and (3, 2a). What is the value of the constant of variation, k?
A.144
B.72
C.36
D.12
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What grade level is "Write and solve inverse variation equations"?
Write and solve inverse variation equations is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Write and solve inverse variation equations?
You'll be able to: Solve for the missing number (variable) in addition and subtraction problems with one-digit numbers, and show your work; Identify the missing number (variable) in an addition or subtraction equation with a box or letter….
Is "Write and solve inverse variation equations" free to practice?
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How many practice questions are included with Write and solve inverse variation equations?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.