Direct Variation

Direct Variation Chapter 5.2

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

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

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 = kx y= ½x y= ½(-6) y = -3

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 y = kx y = 4x 6 = 4x = x 4 4 2

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 = 5.65x y = 5.65(25) y = 141.25

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 = 141.25 y = 5.65x

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 = 20x y = 20(15) y = 300

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?

Direct Variation