1. Inverse, Joint, and Combined Variation Section 8.1 beginning on page 480

2. Making Connections

3. Examples You may be given enough information to write an equation and then have to state what time of variation is occurring between the values. Example 2 (pg. 482): Write an equation for the volume of the prism, and identify the type of variation and the constant of variation. Then find the volume of the prism if the length of the base is 4 inches and the width of the base is 2 inches.

4. Examples You might be told the type of variation, along with additional information (either k or values of x, y, and possibly z) and then have to write an equation and/or find additional values or x, y, and possibly z. Example 1 (pg. 482): The variable y varies inversely as x, and y=13.5 when x=4.5. Find the constant of variation, write an equation for the relationship, and find y when x is 0.5,1,1.5, and 2. What do we know? We have enough info to find k, and then write the equation. The point (4.5,13.5) From this equation, we know that if we divide each x value into 60.75, we will find the corresponding y – value. x0.511.52 y

5. Non-Linear Relationships This is a type of joint variation, specifically, direct variation. [I would accept either answer, but be able to justify them] Use the equation to find each area from the given values of x. x1.52.53.54.5

6. The Tough Stuff Z varies jointly as x and y and inversely as w. Write the appropriate combined-variation equation, and find z for the given values of x, y, and w. Ex: z=54 when x=9,y=2, and w=1.5; x=1.5, y=2.4, and w=3. The variables that vary jointly (or directly) will be in the numerator along with k, and the vary inversely will be in the denominator. Use this info to write the combined variation equation: Use this equation and the given values of x, y, and w to find z

7. Basic Practice

8. Word Problem Practice 1)Write an equation for the volume of a rectangular prism whose base has a length of 12 inches. Identify the type of variation and the constant of variation. Find the volume of the prism if the width of the base is 2 inches and the height of the prism is 4 inches. 2)Write a formula for the area, A, of a circle whose radius is r. Identify the type of variation and the constant of variation. Find the area of the circle when r is 1.5, 2.5, and 3.5. 3)The time, t, that it takes to travel a given distance, d, varies inversely as r, the rate of speed. A certain trip can be made in 7.5 hours at a rate of 60 miles per hour. Find the constant of variation, and write an inverse variation equation. Find t to the nearest tenth when r is 40, 45, 50, and 55. Joint Variation (or direct variation)