- 1. Indirect Variation What is it and how do I know when I see
it?
2. Definition: Yvaries indirectly asxmeans thaty=wherekis the
constant of variation. (Another way of writing this is k = xy)In
other words: *As X increases in value, Y decreases or * As X
decreases in value, Y increases. 3. Examples of Indirect Variation:
Note: X increases, 4, 6, 8 And Y decreases. 12, 8, 6 What is the
constant of variation of the table above? Since y =we can
sayTherefore: 412=k or k = 48 6 8 =k or k = 48 6 8=k or k =48 Note
k stays constant. y = 48/x is the equation! X Y 4 12 6 8 8 6 4.
Examples of Indirect Variation: Note: X decreases, 30, 15, 5 And Y
increases. 5, 10, 15 What is the constant of variation of the table
above? Since y =we can sayTherefore: 30 5=k or k = 150 15 10=k or k
= 150 5 30=k or k =150 Note k stays constant.y = 150/x is the
equation! X Y 30 5 15 10 5 30 5. What is the constant of variation
for the following indirect variation?
X Y 1 9 3 3 9 1 18 .5 6. Is this an indirect variation?If yes,
give the constant of variation (k) and the equation. Yes! k = 24 2
or 48 Equation? y = 48/x X Y 24 2 12 4 2 24 7. Is this an indirect
variation?If yes, give the constant of variation (k) and the
equation. No! The y-values decrease, but then increase! The k
values are also different! X Y 7 5 15 2 20 2.5 8. Which is the
equation that describes the following table of values?
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32 Answer Now X Y 50 4 20 10 10 20 9. Using
Indirect Variation to find unknowns (y = k/x) Given that y varies
indirectly with x, and y = 12 when x=4,Find y when x = 12.HOW???2
step process 1. Find the constant variation k = xy or k = 12 4 =
48k=48 2. Use y = k/x. Find the unknown (y). y=48/12y= 4 Therefore:
Y =4 when X=12 X Y 4 12 12 ? 10. Given that y varies indirectly
with x, and y = 100 when x=25, Find x when y = 500.HOW???2 step
process 1. Find the constant variation. k = yx or k = 100 25K =
2500 2. Use y = k/x. Find the unknown (x). 500 = 2500/xx = 5
Therefore: X = 5 when Y = 500 Using Indirect Variation to find
unknowns (y = k/x) X Y 25 100 500 11. Indirect Variation and its
graph With indirect variation the equationis y = k/x Note:Because
one variable is always doing the opposite of the other variable,
the graph will never go through. 12. the ORIGIN!!!!! 13. The graph
of Indirect Variation 14. Using Indirect Variation to solve word
problems Problem: A gas with volume 45 cubic inches is under a
pressure that is 75 pounds per square inch. Find the pressure when
the volume is 80 cubic inches. Step One : Find points in table.
Step Two: Find the constant variation and equation: k = xy or k =
45 75 = 3375 y =3375/x Step Three: Use the equationto find the
unknown. y = 3375/80y = 42.1875 X (volume) Y (pressure) 45 75 80 ?
15. Using Indirect Variation to solve word problems Problem: A gas
with volume 30 cubic inches is under a pressure that is 40 pounds
per square inch. Find the pressure when the volume is 60 cubic
inches. Step One:Find points in table. Step Two: Find the constant
variation. k = xy or k = 30 40 = 1200 k = 1200 Step Three: Use the
equationto find the unknown. y=k/x y = 1200/60 y = 20 X (volume) Y
(pressure) 30 40 60 ? 16. Mini Quiz
- Is this an indirect variation?If yes, give the constant of
variation (k) and the equation.
- Given that y varies indirectly with x, and y =8 when x=1.5,Find
y when x = 3.
- Find an equation of indirect variation where y varies
indirectly as x. One pair of values isy = 15 when x = 8.
X Y 4 7 6 42/3 8 3 17. Mini Quiz Continued
- 4. The time (t) required to do a certain job varies inversely
as the number (n) of people working (assuming all work at the same
rate). It takes 4 hours for 20 people to wash and wax the floors in
a building. Find the equation of variation.
- 5. It takes 16 hours for 2 people to resurface a gym floor. How
long would it take 6 people to do the job?
18. Compare and Contrast Direct and Indirect Variation
- How to find the constant of variation
