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

Summary

This video explains inverse variation, covering its definition, equation, graph, and how to express statements as mathematical equations. It also demonstrates how to find the constant of variation and write equations representing inverse relationships, concluding with examples of solving for missing variables in inverse variation problems.

Highlights

Introduction to Inverse Variation00:00:02

The video introduces the topic of inverse variation, outlining what will be covered, including different forms of inverse variation (equations, graphs, tables, and statements), finding the constant of variation, and developing equations for inverse relationships.

Defining Inverse Variation and its Formula00:00:33

Inverse variation is defined as a relationship where the product of two quantities' corresponding values is a constant. The formula for inverse variation is y = K/x, where K is the constant of variation. The formula to find K is K = xy.

Statements, Graphs, and Tables of Inverse Variation00:01:52

Common statements for inverse variation are "y varies inversely as x" or "y is inversely proportional to x." The graph of inverse variation is not a straight line, as seen in direct variation. In a table of values, as one variable (x) increases, the other variable (y) decreases, which is the opposite behavior of direct variation.

Expressing Inverse Variation as Mathematical Equations00:03:50

The video provides examples of how to convert real-world statements into inverse variation equations. For instance, 'the number of pizza slices P varies inversely as the number of persons N' translates to P = K/N. Similarly, 'the number of persons N needed to do a job varies inversely as the number of days D' becomes N = K/D.

Finding the Constant of Variation and the Equation (Examples 1-3)00:07:29

The video demonstrates how to find the constant of variation (K) and write the equation for an inverse relationship. For example, if y varies inversely as x, and y = 12 when x = 5, then K = 5 * 12 = 60, and the equation is y = 60/x. Another example involves fractional values, and a table of values is used to confirm the constant of variation by checking if xy is constant for all pairs.

Solving for Missing Variables in Inverse Variation (Examples 1-2)00:12:18

The final section explains how to solve for an indicated variable in an inverse variation problem. Given y varies inversely as x, y=3 when x=4, the constant K is found to be 12. Then, to find y when x=6, the new equation y = 12/x is used, resulting in y = 2. A second example with variables R and S where R=100 and S=27 is solved similarly to find R when S=45.