Algebra 1 Common Core Student Edition, Grade 8-9

G o t It? 5. Does each situation rep resen t a direct variation or an inverse v ariatio n?

Explain your reasoning.

a. You buy sw eaters in a clothing store for $35 each.

b. You walk 5 m i each day. Your speed an d tim e spent walking vary each day.

Lesso n Ch eck

you know HOW?

Suppose y varies inversely w ith x, and y = — 3 when

x = 17. W hat is an eq u a tio n for the inverse variation?

An 80-lb weight is placed on a lever, 9 ft from the

fulcrum. W hat am o u n t of w eight should you p u t 6 ft

from the fulcrum to balance th e lever?

W hat is the graph of y =

Do the d ata in the table rep resen t a

direct variation or an inverse variatio n?

Write an equation th at m odels the data.

-6

-9

12

18

Do you UNDERSTAND?

MATHEMATICAL

PRACTICES

Xy

5. Vocabulary Is the equ atio n y = 5 an inverse
   variation? If so, w hat is th e co n stan t of variation?


6. Does th e graph of an inverse variation always,
   sometimes, or never pass through the origin? Explain.


7. Reasoning Suppose you place two different weights
   on a lever. W hich weight m u st be closer to the
   fulcrum in o rder for th e lever to balance? Explain.


8. R e a s o n i n g Suppose th e price p e r pencil at an office
   supply store decreases as th e n u m b e r of pencils you
   buy increases. Does the price p e r pencil necessarily
   vary inversely w ith th e n u m b e r of pencils bought?
   Explain.

Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses

MATHEMATICAL

PRACTICES

1^1 Practice Suppose y varies inversely with x. Write an equation for the inverse variation. ^ See Problem 1.

9. y=6w henx=3 10. y = 1 w h e n x = — 2 11. y = 7 w h e n x = 8


10. y = 3 w h e n x = 0.5 13. y = —1 0 w h e n x = —2.4 14. y = 3 .5 w h e n x = 2.2


11. Travel A family takes 2 1 h to drive from th eir h o u se to a lake at 48 m i/h. The See Problem 2.
    travel tim e varies inversely w ith th e speed of th e car. How long will the retu rn trip
    take at 40 m i/h?


12. Bicycling A cam per takes 2 h to ride a bike aro u n d a reservoir at 10 mi/h at the
    beginning of the sum m er. By th e en d of th e sum m er, she can ride a ro u n d the
    reservoir in 1 \ h. The tim e to travel aro u n d th e reservoir varies inversely w ith the
    speed she pedals. W hat is h er speed at th e en d of th e sum m er?

Graph each inverse variation.

17. y = | 18. xy = 12


18. 20 = xy 22. y =^15 x

19

23. xy = -2 4

4L See Problem 3.

on 14

20- ~x=y

24.y = ^

702 Chapter 11 Rat io nal Expressions and Funct ions