5-5 Direct Variation

Ex. 1 Is Direct Variation?

• Direct Variation is the equation y = kx, where k is any constant or number

• Is 5x + 2y = 0 direct variation?• Solve for y

• Yes

• Is 5x + 2y = 9 Direct Variation?

• No • Hint: If x y = 0, then will be

direct. If x y 0, then will not be direct.

Your Practice

Is 3y + 4x = 8 an example of direct variation?No, does not equal zero.

• Is 7y = 2x an example of direct variation?

• Yes, y = x no number after the x

Ex. 2 Writing an Equation

• Write an equation of the direct variation that includes the point (4,-3).

• Point written (x,y)• Plug in x and y into y = kx to find k– -3 = k(4)

• Plug k into y = kx– y = x

Your Practice

• Write an equation of the direct variation that includes the point (-3,-6).

• Plug -3 in for x and -6 in for y into y = kx– -6 = k(-3)

– 2 = k– y = 2x

Ex. 3 Story Problems• Your distance from lightning varies directly with the time it takes you to hear

thunder. If you hear thunder 10 seconds after you see lightning, you are about 2 miles from the lightning. Write an equation for the relationship between time and distance.

• Whatever comes before “varies directly” is y– y = 2

• Whatever comes after “varies directly” is x– x = 10

• Put into y = kx to find k and write equation– 2 = k(10)– 2 = 10k– 10 10– 1 = k– 5

• So y = 1/5k

Your practice• A recipe for a dozen corn muffins calls for 1 cup of flour. The number of muffins

varies directly with the amount of flour you use. Write a direct variation equation for the relationship between the number of cups of flour and the number of muffins.

• What comes before “varies directly”– muffins

• y = 12• What comes after “varies directly”

– Cups of flour• x = 1

• y = kx– 12 = k(1)– – 12 = k– y = 12x

Ex. 4 Direct Variation and Tables• To determine if direct variation, check for each x and y in that row• If is the same all the way down, then it is direct variation• k

• K = -.75• So y = -.75x

x y y/x decimal-3 2.25 2.25/3 -0.751 -0.75 -.75/1 -0.754 -3 -3/4 -0.756 -4.5 -4.5/6 -0.75

Your Practice

• Is the table show direct variation and if so, what is the equation?

• Check y/x and decimal to be the same

• k = 1.8• y = 1.8x

x y3 5.47 12.6

12 21.6

y/x decimal5.4/3 1.8

12.6/7 1.821.6/12 1.8