1. EXAMPLE 2 Graph direct variation equations
b. Write the equation for this line / graph

2. GUIDED PRACTICE for Examples 2 and 3
5. The graph of a direct variation on equation passes
through the point (4,6). Write the direct variation
equation and find the value of y when x =24.
SOLUTION
Because y varies directly with x, the equation has
the form y = ax. Use the fact that y = 6 when x = 4
to find a.
y = ax Write direct variation equation.
6 = a (4) Substitute.
6 3 Solve for a.
a= =
4 2

3. GUIDED PRACTICE for Examples 2 and 3
ANSWER
A direct variation equation that relates x
and y is y = 3 x when x = 24. y = 3 (24) = 36
2 2

4. Graph these
equations. What
can you say about
these lines?
y = 2/3 x
y= -3/2 x

5. • If the variables x & y vary directly, write an
equation when x = 5 and y = 20.
• (think y = ax)
• So, would 20 = a(5)
• Equation : y = 4x

6. • If the variables x & y vary directly, write an
equation when x = -3 and y = 30.
• What would be the value of y when x = 5?

7. EXAMPLE 4 Solve a multi-step problem
SALTWATER AQUARIUM
The number s of tablespoons of
sea salt needed in a saltwater fish
tank varies directly with the
number w of gallons of water in
the tank. A pet shop owner
recommends adding 100
tablespoons of sea salt to a 20
gallon tank.
• Write a direct variation equation that relates w and s.
• How many tablespoons of salt should be added to a
30 gallon saltwater fish tank?

8. • When x and y vary directly, there is a
nonzero number a such that the following
is true:
y = ax
a is the constant of variation
For example: y = 3x or y = -1/4x
non-example : y = 4x + 5

9. Graph these
equations. What
can you say about
these lines?
y = 2/3 x
y= -3/2 x

10. • If the variables x & y vary directly, write an
equation when x = 5 and y = 20.
• (think y = ax)
• So, would 20 = a(5)
• Equation : y = 4x

11. • If the variables x & y vary directly, write an
equation when x = -3 and y = 30.
• What would be the value of y when x = 5?

12. • Cont’ P. 257 (#23-27, 29-33, 40-42)
• (45 together)
Cost
In
Dollars
Number of days

13. x 1 2 3 4 6
y 5 10 15 20 30
Tell if the table represents direct variation. If
so, write the direct variation equation.