1. Equation of Direct Variation
In a DIRECT VARIATION, as one quantity increases, the other quantity increases.
Equation of Direct Variation

2. To solve a problem using direct variation, we used proportions.
If Martha can run 10 miles in 140 minutes, how long will it take her to run 26 miles.

3. Electrical current and Resistance
INVERSE VARIATION
In an INVERSE VARIATION, as one quantity increases, the other quantity decreases.
EXAMPLES
Rate of speed and time
Pressure and Volume
Electrical current and Resistance

4. Equations of Inverse Variation
In an INVERSE VARIATION, as one quantity increases, the other quantity decreases.
Equations of Inverse Variation

5. y varies inversely as x. If y = 20 when x = 12, find y when x = 45.
INVERSE VARIATION
y varies inversely as x. If y = 20 when
x = 12, find y when x = 45.
METHOD #1: Find Constant of Variation

6. y varies inversely as x. If y = 20 when
INVERSE VARIATION
y varies inversely as x. If y = 20 when
x = 12, find y when x = 45.
METHOD #1: Product Rule

7. y varies inversely as x. If y = 10 when x = 6, find y when x = 12.
INVERSE VARIATION
FLASH CARDS
y varies inversely as x. If y = 10 when x = 6, find y when x = 12.
x is twice as large, so….?
y = 5

8. y varies inversely as x. If y = 8 when x = 20, find y when x = 10.
INVERSE VARIATION
FLASH CARDS
y varies inversely as x. If y = 8 when x = 20, find y when x = 10.
x is half as large, so….?
y = 16

9. y varies inversely as x. If y = 12 when x = 18, find y when x = 15.
INVERSE VARIATION
FLASH CARDS
y varies inversely as x. If y = 12 when x = 18, find y when x = 15.
Calculators? Nearest tenth!
y = 14.4

10. y varies inversely as x. If y = 13 when x = 31, find y when x = 14.
INVERSE VARIATION
FLASH CARDS
y varies inversely as x. If y = 13 when x = 31, find y when x = 14.
Calculators? Nearest tenth!
y = 28.8

11. A ratio of two polynomial expressions is called a RATIONAL EXPRESSION.
RATIONAL EXPRESSIONS
A ratio of two polynomial expressions is called a RATIONAL EXPRESSION.
EXAMPLES

12. You might call it “cancelling” or “reducing”
RATIONAL EXPRESSIONS
To simplify a rational expression, divide the numerator and denominator by their GCF.
You might call it “cancelling” or “reducing”

13. RATIONAL EXPRESSIONS
To simplify a rational expression, divide the numerator and denominator by their GCF.
Excluded Values?

14. RATIONAL EXPRESSIONS EXCLUDED VALUES are values of x that
make the expression undefined…
…in other words, turns the denominator equal to zero…
…and division by zero is undefined.

15. State the excluded values for: Set denominator equal to zero and solve
RATIONAL EXPRESSIONS
State the excluded values for:
Set denominator equal to zero and solve

16. State the excluded values for: Set denominator equal to zero and solve
RATIONAL EXPRESSIONS
State the excluded values for:
Set denominator equal to zero and solve

17. State the excluded values for: Set denominator equal to zero and solve
RATIONAL EXPRESSIONS
State the excluded values for:
Set denominator equal to zero and solve

18. Simplify each expression and state the excluded values
RATIONAL EXPRESSIONS
Simplify each expression and state the excluded values

19. Simplify each expression and state the excluded values
RATIONAL EXPRESSIONS
Simplify each expression and state the excluded values

20. RATIONAL EXPRESSIONS
TRY THIS ONE

21. RATIONAL EXPRESSIONS
MORE PRACTICE

22. RATIONAL EXPRESSIONS
MORE PRACTICE

23. RATIONAL EXPRESSIONS
MORE PRACTICE