Direct Variation Chapter 5.2

Coefficient of Variation Direct Variation Equation of Direct Variation y = kx y = kx Coefficient of Variation

Direct Variation When you see: “y varies direcly as x” write y = kx

y = -3x y = kx y = kx Direct Variation Write the equation of direct variation that has a equal to -3 Replace k with -3 coefficient of variation y = -3x y = kx y = kx

y = -3 y = ½(-6) y = kx y = ½x Direct Variation Assume If the coefficient of variation is ½, then what is the value of y when x = -6? Replace k with ½ Replace x with -6 Multiply ½ times -6 to get answer y varies directly as x. y = -3 y = ½(-6) y = kx y = ½x

3 6 = 4x y = 4x y = kx = x 2 4 4 Direct Variation Assume y varies directly as x. If the coefficient of variation is 4, then what is the value of x when y = 6? Replace k with 4 and y with 6 Divide 4 on both sides Reduce the fraction 3 6 = 4x y = 4x y = kx = x 2 4 4

Direct Variation Suppose y varies directly as x. If y = 3 when x = 15, then find x when y = 5. Suppose y varies directly as x. Find x when y = 10 if y = -7 when x = -14. Suppose y varies directly as x. If x = 15 when y = 12, find x when y = 21. Suppose y varies directly as x. If x = 24 when y = 8, then what is the coefficient of variation?

Direct Variation Word Problems The amount of a person’s paycheck varies directly with the number of hours worked. For 13 hours of work, the paycheck is $73.45. Find the pay for 25 hours of work. “varies directly” means: Remember, “y” always varies directly as “x” y = kx

Direct Variation Word Problems The amount of a person’s varies directly with the number of For 13 hours of work, the paycheck is $73.45. Find the pay for 25 hours of work. If “y” varies directly as “x” than what comes before varies directly is y and what comes after it is x paycheck hours worked.

Direct Variation Word Problems The amount of a person’s paycheck varies directly with the number of hours worked. For 13 hours of work, the paycheck is $73.45. Find the pay for 25 hours of work. Replace paycheck with $73.45 and hours with 13 Paycheck = k(hours) 73.45 = k(13)

Direct Variation Word Problems Divide both sides by 13 Plug k back into the equation 73.45 = k(13) 5.65 = k 13 13 y = 5.65x

Direct Variation Word Problems The amount of a person’s paycheck varies directly with the number of hours worked. For 13 hours of work, the paycheck is $73.45. Find the pay for 25 hours of work. The question asks for how much you’d make in 25 hours, so replace x with 25 Multiply to get your answer y = 141.25 y = 5.65x y = 5.65(25)

Direct Variation Word Problems The amount of a person’s paycheck varies directly with the number of hours worked. For 13 hours of work, the paycheck is $73.45. Find the pay for 25 hours of work. K = 5.65 which is how much this person makes per hour. For 25 hours, this person makes $141.25 y = 5.65x y = 141.25

Direct Variation Word Problems The number of calories in a container of milk is directly proportional to the amount of milk in the container. If there are 160 calories in an 8-ounce glass of milk, find the number of calories in a 15-ounce glass of milk. Directly proportional means direct variation y = kx

Direct Variation Word Problems The number of calories in a container of milk is directly proportional to the amount of milk in the container. If there are 160 calories in an 8-ounce glass of milk, find the number of calories in a 15-ounce glass of milk. Y varies directly as x, so calories is y and amount of milk is x y = kx calories = k(amt of milk)

Direct Variation Word Problems The number of calories in a container of milk is directly proportional to the amount of milk in the container. If there are 160 calories in an 8-ounce glass of milk, find the number of calories in a 15-ounce glass of milk. Calories is 160 and the amount of milk is 8 calories = k(amt of milk) 160 = k(8)

Direct Variation Word Problems 160 = k(8) 20 = k y = 20x Divide both sides by 8 Plug k back into the equation 8 8

Direct Variation Word Problems The number of calories in a container of milk is directly proportional to the amount of milk in the container. If there are 160 calories in an 8-ounce glass of milk, find the number of calories in a 15-ounce glass of milk. K means 20 calories per ounce Plug in 15 for x to solve the problem Multiply to solve y = 300 y = 20x y = 20(15)

Direct Variation Word Problems The number of calories in a container of milk is directly proportional to the amount of milk in the container. If there are 160 calories in an 8-ounce glass of milk, find the number of calories in a 15-ounce glass of milk. There are 300 calories in a 15-ounce glass of milk y = 300

Direct Variation Word Problems Laura typed 176 words correctly in 4 minutes. Assuming a direct variation, how many words can she type in 30 minutes? A refund you get varies directly as the number of cans you recycle. If you get a $3.75 refund for 75 cans, how much should you get for 500 cans?

Direct Variation Word Problems The number of miles driven varies directly with the number of gallons of gas used. Erin drove 297 miles on 9 gallons of gas. How far would she be able to drive on 14 gallons of gas? The kinetic energy of a car varies directly with the square of the velocity of the car. A car with a velocity of 9 meters per second has 33,100 joules of kinetic energy. About how much kinetic energy does the same car have when traveling at 12 meters per second?

Direct Variation Word Problems The height of a kite from the ground varies directly with the cube of the wind speed. A kite flies 8 feet high when the wind speed is 10 miles per hour. What is the height of a kite when the wind speed is 25 miles per hour?