Lesso n Ch eck
Do yo u k n o w H OW?
- Does the equation 6y = 18x rep resen t a direct
variation? If it does, w hat is its co n stan t of variation? - Suppose y varies directly w ith x, an d y = 30 w hen
x = 3. W hat direct variation equation relates x a n d y? - A recipe for 12 corn m uffins calls for 1 cup of flour.
The n u m b er of m uffins you can m ake varies direcdy
w ith the am o u n t of flour you use. You have 2^ cups of
flour. How m any m uffins can you make? - Does y vary direcdy w ith x? If it
does, w hat is an equation for the
direct variation?
MATHEMATICAL
Do y o u UN DERSTAND? PRACTICES
Vocabulary Determine whether each statement is
always, sometimes, or never t r u e.- The ordered p air (0, 0) is a solution of the direct
variation e q u a tio n y = kx. - You can write a direct variation in th e form
y = k + x, where k # 0. - The co n stan t of variation for a direct variationy
re p resen te d by y = kx is
8. R e a s o n i n g Suppose q v a r i e s d i r e c t ly w i t h p. Does
this im ply th a t p v a r i e s d i r e c t l y w i t h ql Explain.1-2 1
2 -1
4 -2& Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses
Practice Determine whether each equation represents a direct variation. If it does, find See Problem 1.
the constant of variation.- 2y = 5x + 1 10. 8x+9y=10 11. -12x= 6y
- y + 8 = - x 13. - 4 + 7x + 4 = 3y 14. 0 .7 x - 1.4y = 0
Suppose y varies directly with x. Write a direct variation equation that relates See Problem 2.
x and y. Then find the value of y when x = 12.- y = - 1 0 w h e n x = 2. 16. y = 7 |w h e n x = 3. 17. y = 5 w h e n x = 2.
- y = 125 w h e n x = — 5. 19. y = 10.4 w h en x = 4. 20. y = w h e n x = —
Graph each direct variation equation. ^ See Problem 3.- y = 2x 22. y=|x 23. y=-x 24. y = - | x
- Travel Time The distance d you bike varies directly w ith th e a m o u n t of tim e t you
bike. Suppose you bike 13.2 m i in 1.25 h. W hat is an eq u a tio n th a t relates d a n d tl
W hat is th e graph of th e equation? - Geometry The p erim e te r p of a regular hexagon varies directly w ith th e length i of
one side of th e hexagon. W hat is an equ atio n th a t relates p a n d €? W hat is th e graph
of the equation?
304 Chapter 5 Linear Funct ions