Inverse Variation - Constant of Variation and Equation - Grade 9 Math Second Quarter

Summary

In this video, Teacher Gone explains the concept of inverse variation, where the product of two variables is a constant. The lesson covers how to express inverse variation in equations, graphs, and tables, and how it contrasts with direct variation. The video also demonstrates how to find the constant of variation (K) and solve problems using the formula Y = K/X. Several real-life examples, such as sharing pizza slices and job completion times, are used to illustrate inverse variation. Lastly, the teacher shows how to convert statements into mathematical equations and solve for missing variables.

Takeaways

• 📚 Inverse variation occurs when the product of two quantities is constant, meaning one quantity increases as the other decreases.
• 📐 The equation for inverse variation is y = K / x, where K is the constant of variation.
• 🔢 The formula to calculate the constant of variation is K = x * y.
• ✏️ Statements like 'Y varies inversely as X' or 'Y is inversely proportional to X' both mean y = K / x.
• 📈 The graph of inverse variation is not a straight line; it forms a curve, unlike direct variation which is linear.
• 🧮 In a table of values for inverse variation, as x increases, y decreases, showing the inverse relationship.
• 🍕 Example: The number of pizza slices per person decreases as more people share the pizza, representing inverse variation.
• 👷 Inverse variation can also describe relationships like the number of people working on a job and the days required to complete it.
• ✍️ To find the constant of variation, multiply corresponding values of x and y, and then use the equation y = K / x.
• 🔍 Real-world examples include costs per person in shared resources and work time based on the number of workers.

Q & A

What is the definition of inverse variation?

Inverse variation occurs when the product of corresponding values of two quantities is a constant. In this relationship, one quantity varies inversely as the other.

What is the formula for inverse variation?

The formula for inverse variation is y = k / x, where k is the constant of variation, and x and y are the two variables.

How can you calculate the constant of variation in an inverse variation?

The constant of variation k can be calculated using the formula k = x * y. This is the product of the two variables in the inverse relationship.

How does the graph of inverse variation differ from direct variation?

In an inverse variation, the graph is a hyperbola, which differs from the straight line of direct variation that passes through the origin.

What happens to the values of y as x increases in an inverse variation?

In an inverse variation, as the value of x increases, the value of y decreases.

How would you express the statement 'The number of pizza slices varies inversely as the number of people sharing' in a mathematical equation?

The equation would be p = k / n, where p is the number of pizza slices, n is the number of people sharing, and k is the constant.

If the number of people required to do a job varies inversely as the number of days to finish the job, how would you express this in a mathematical equation?

The equation would be n = k / d, where n is the number of people and d is the number of days, with k as the constant of variation.

How do you find the equation representing an inverse variation if you know that y = 12 when x = 5?

First, calculate the constant k = x * y = 5 * 12 = 60. The equation representing the inverse variation is y = 60 / x.

In an inverse variation problem, if y = 3 when x = 4, how do you find y when x = 6?

First, calculate the constant k using k = x * y = 4 * 3 = 12. Then, to find y when x = 6, use y = 12 / 6 = 2.

What is the process for finding the constant of variation and the equation for an inverse variation when given a table of values?

First, calculate the constant of variation k using k = x * y for each pair of values in the table. If the product is consistent, this is the constant. Then, the equation is y = k / x, where k is the constant.