Lesson 35 Section 6.8Examine this table:# hours worked Pay1 $82 $163 $244 $326 $4910 $80When a relation between pairs of numbers is a constant ratio, such as above; it is called a Direct Variation. The ratio above is 18 and we say the pay varies directly as hours. The number 8 from the ratio is called the variation constant. The Variation Equation ishp 8, where p represents pay and h represents hours.Direct Variation is of the form kxy . We say y varies directly as x or y is directly proportional to x. The number k is the variation constant or the constant of proportionality.1) The value of y varies directly as x. If y = 5 when x = 12, find the value of the variation constant and the resulting variation equation.2) The value of b is directly proportional to a. If b = 12 when 31a, find the constant of proportionality and the resulting variation equation.Examine this table:bus speed time of trip20 mph 1 hr.40 mph ½ hr.6031 hr.80 ¼ hr.When a relation between pairs of numbers is such that the product of the numbers remains constant, such as the table above (product is 20), it represents Inverse Variation.The product 20 represents the variation constant and the inverse variation is rt20, where t represents time and r represent speed.Inverse Variation is of the form xky . We say y varies inversely as x or y is inversely proportional to x. The number k is still the variation constant or the constant of proportionality.3) Suppose y varies inversely as x. If y = 16 when x = 4, find the variation constant and the resulting variation equation.4) Let n be inversely proportional to m. Suppose n = 81 when m = 4. Find the constant of proportionality and the resulting variation equation.Joint Variation is of the form kxzy .Combined Variation is of the form zxky .5) Suppose y varies jointly as x and z. a) If y = 6 when x = 12 and z = 4, find the variation constant and the resulting variation equation.b) Use your equation to find the value of y when x = 3 and z = 4.6) Let y vary jointly as x and z and inversely as w.a) If y = 20 when x = 2, z = 21, and w = 10, find the variation constant and the resulting variation equation.b) Find the value of y if x = 4, z = 0.6, and w = 0.3.7) Suppose y varies directly as the square of x and inversely as the square root of z.a) If y = 12 when x = 3 and z = 16, find the value of the variation constant and the resulting equation.b) Find the value of y if x = 2 and z = 9.8) The time T required to do a job varies inversely as the number of people P working. It takes 5 hours for 7 volunteers to pick up trash from 1 mile of a highway. How long would it take 10 volunteers to complete the job?9) The electric current I, in amps, in a circuit varies directly as the voltage V. When 16 volts are applied, the current is 5 amps. What is the current when 20 volts are applied?10) The stopping distance d of a car (in feet) after the brakes have been applied varies directly as the square of the speed r. Once the brakes are applied, a car traveling 60 miles per hour can stop in 138 feet. What stopping distance corresponds to a speed of 40
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