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

DIRECT VARIATION 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.

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

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

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

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

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

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

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

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

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

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

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

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.

RATIONAL EXPRESSIONS 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

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

RATIONAL EXPRESSIONS Simplify each expression and state the excluded values

RATIONAL EXPRESSIONS Simplify each expression and state the excluded values

RATIONAL EXPRESSIONS TRY THIS ONE

RATIONAL EXPRESSIONS MORE PRACTICE

RATIONAL EXPRESSIONS MORE PRACTICE

RATIONAL EXPRESSIONS MORE PRACTICE