Slope and Direct Variation

Lesson 5-2

 

____________ ______________ is an equation in the form of ________,

where k≠0. In the equation y = kx, ____ is the ______________________.

(k is always equal to the __________________ .) Direct variation is also

known as a direct __________________________.

Direct variation y = kx

k constant of variation

slope

proportion

1

up 1 right 1

A direct variation will ALWAYS pass through the origin.

Graph y = 2x

m = _______

•Remember, the first point will always be (0,0) in a direct variation.•Find additional points using the slope.

up 3

left 2

Moving up 2 and left 3 will fall on the same line as moving down 2 and right 3.

y = kx

9 -3 9 = k (-3)

-3 = k

y = -3x

y = -3x

15 = -3x

-5 = x

y = kx

15 = k(5)

15/5 = 5k/5

3 = k

y = 3x

y = 3x

-45 = 3x

-45/3 = (3x)/3

-15= x

Practice: Write a direct variation equation that relates x and y. Assume that y varies directly as x. Then solve.

7. If y = 27 when x = 6, 8. If y = 10 when x = 9, find x when y = 45. find x when y = 9. ________________________ ____________________

________________________ ___________________

________________________ ______________________

________________________ ______________________

 ________________________ ______________________

________________________ ______________________

________________________ ______________________

Practice: Write a direct variation equation that relates x and y. Assume that y varies directly as x. Then solve.

9. If y = -7 when x = 14, 10. find y when x = 20.  ________________________ ______________________

________________________ ______________________

________________________ ______________________

________________________ ______________________

 ________________________ ______________________

________________________ ______________________

________________________ ______________________

Using Direct Variations to Solve ProblemsThe Ramirez family is driving cross-country on vacation. They drive 330 miles in 5.5 hours.

A. Write a direct variation equation to find the distance driven for any number of hours.

y = 60 x

10 hours

 A flock of geese migrated 375 miles in 7.5 hours. A. Write a direct variation equation to find the distance flown in any time. 

y = 50 x

B. Estimate how many hours of flying time it would take the geese to migrate 3000 miles.

y = distance, x = time in hours

y = 50 x

3000 = 50 x

60 hours = x