Inverse Variation Chapter 8 Section 8.10

Objective Students will use inverse variation to solve problems

Concept The table shows the time t, that it takes a car to travel a distance of 40 mi at the speed of r mi/h. You can see that rt = 40. Notice that if the speed is increased, the time is decreased, so that the product is always 40. You can say that the time varies inversely as the rate. Rate Time 20 2 30 4/3 40 1 50 4/5

Concept An inverse variation is a function defined by an equation of the form xy = k, where k is a nonzero constant, or y = k/x, where x ≠ 0 You say that y varies inversely as x or that y is inversely proportional to x. The constant k is the constant of variation

Concept Let (x1, y1) and (x2, y2) be two ordered pairs of the same inverse variation. Since the coordinates must satisfy the equation xy = k, you know that x1y1 = k and x2y2 = k, or x1y1 = x2y2 You can compare the equations for direct variation and inverse variation

Concept Direct Variation Inverse Variation y = kx xy = k, or y = k / x y1 / x1 = y2 / x2 x1y1 = x2y2

Concept The equations show that for direct variation the quotients of the coordinates are constant and for inverse variation the products of the coordinates are constant

Find the missing value m1 = 24, d1 = 30, m2 = 45, d2 = ? Example Find the missing value m1 = 24, d1 = 30, m2 = 45, d2 = ?

Find the missing value x1 = 20, y1 = 7, x2 = 4, y2 = ? Example Find the missing value x1 = 20, y1 = 7, x2 = 4, y2 = ?

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