Algebra 1 Common Core Student Edition, Grade 8-9

Think

How can you check

the reasonableness

of your answers?

Substitute each x-value

from the table into the

equation and find the

corresponding value of y.

The y-values given by the

equation should match

the y-values in the table.

To answer these
problems, you may find
it helpful to first make
a table of values. In
part (A), for instance,
let x be the number of
friends and let y be the
cost per person.

Problem 4 Determining Direct or Inverse Variation

Do the data in each table represent a direct variation or an inverse variation? For

each table, write an equation to model the data.

The values of y seem to vary directly w ith th e values ofx. C heck each ratio

Q

OB

3-15

4 -20

5-25

mmm

(^29)
44.5
6 3
-15= -5 -20
4
-25
5 -5
y
The ratio j is th e sam e for all d ata pairs. So this is a direct variation,
and k = - 5.
An eq u a tio n is y = —5x.
The values o fy seem to vary inversely w ith the values of x. Check each
product xy.
2(9) = 18 4(4.5) = 18 6(3) = 18
The p ro d u c t xy is the sam e for all d ata pairs. So this is an inverse
variation, and k = 18.
An eq u a tio n is xy = 18, or y:

• G o t It? 4. Do th e d ata in each table re p resen t a direct variation or an inverse
  variation? For each table, w rite an equation to m odel th e data,
  a. b.
  4 -12
  6 -18
  8 -2 4
  an
  (^4) -12
  (^6) -8
  (^8) -6
  Id en tifyin g Direct o r Inverse V ariatio n
  Does each situation represent a direct variation or an inverse variation? Explain
  your reasoning.
  Q Boating The cost of a $120 boat rental is split among several friends.
  The cost p er p erso n tim es th e n u m b e r of friends equals th e total cost of th e boat
  rental. Since th e total cost is a co n stan t p ro d u c t of $120, th e cost p er perso n varies
  inversely w ith th e n u m b e r of friends. This is a n inverse variation.
  0 Entertainment You download several movies for $14.99 each.
  The cost p er dow nload tim es th e n u m b e r of movies dow nloaded equals the total
  cost of th e dow nloads. Since th e ratio numberof monies downloaded is co n stan t at
  $14.99, th e total cost varies directly w ith th e n u m b e r of m ovies dow nloaded. This is
  a direct variation.
  Problem 5
  c
  Po w er A lg eb r a.co m j L e s s o n 1 1 - 6 Inverse Variat io n 701