Textbook 9-1
Objective:
a. Write and use direct variation models.
b. Write and use inverse variation models.
Direct Variation or Directly Proportional

x and y show direct variation if

k is called the constant of variation

The graph of y = kx goes through the origin.

Example Formula is d=rt
Distance and time vary directly, which means as time increases, distance
increases.

Another Example:
The number of hours you work varies directly with the amount of pay
you earn. (The more you work, the more you get paid)
The variables x and y vary directly. Write an equation that relates the
two variables.
Then find y when x = 6
1.) x = 2, y = 8
2.) x = 24, y = 6
What would the graph of each equation look like?
3.) x = .8, y = -1.6
Inverse Variation / Inversely Proportional

x and y show inverse variation if

Example Formula is density = mass/volume
Density and volume vary indirectly, which means as volume increases,
density decreases.

Another Example:
The number of people renting a limo varies inversely with the amount of
money each person has to pay to rent the limo. (The more people riding
in the limo, the less each person has to pay)
The variables x and y vary inversely. Use the given values to write an
equation relating x and y.
Then find y when x = 4
4.) y = 6, x = 3
5.) y = -7.5, x = 2
6.) y = 2, x = 8
Sample Problems:
1.)
In a relationship, y varies directly with x. What happens to the value of y if x
is doubled?
2.)
In a relationship, y varies inversely with x. What happens to the value of y if x
is tripled?
3.)
y is directional proportional to x. If y = 30 when x = 25, find the constant of
4.)
y is inversely proportional to x. If y = 45 when x = 81, find the constant of
variation.
variation.