Proportion to Powers of a Variable

1. Proportion to Powers of a Variable Slideshow 24, Mathematics Mr Richard Sasaki, Room 307

2. Objectives • Review Direct Proportion (Grade 7) • Understand how to calculate a constant for where • Be able to solve problems where variable

3. Direct Proportion As you know, there are two main types of proportion. Direct Proportion Inverse Proportion and . ‘’ Direct proportional is represented by the symbol . An equation representing direct proportion is in the form where . If is unknown, but we have a value for and at a point, we can calculate (which is constant for all points).

4. Direct Proportion Example Two variables exist where . At a point, when , . Show there exists a specific equation for in terms of and calculate when . As, there exists some relation for all . For when , , we get . As holds for all and , for all . When .

5. When When When When As, there exists some relation for all . For when , , we get . As holds for all and , for all . A pencil costs the same, no matter how many are bought. When .

6. Direct Proportion withOther Powers We know that if two variables exist where , this implies for all . If is directly proportional to the square of , this can be represented as . For some unknown value where , this relationship implies that . In fact, the same implication applies for any power. If , where , we can say that .

7. Direct Proportion withOther Powers Example Two variables exist where . At a point, when , . Find a specific equation for in terms of and calculate when . . As when and , , we get . When , . Try the next worksheet! わんわんわん。

8. When When When When Meow.

9. Real World Regular Proportion Problems Try to solve some of the problems like the one below applying your general understanding of proportion. Example Tojiro walks at a constant speed for 15 minutes and covers three-quarters of a kilometre. How fast was he walking? Please give your answer in kilometres per hour. Hi! I’m Tojiro! My name is Ryoma.

10. Hi! I’m Tojiro! My name is Ryoma.