2.3: Direct Variation
If a man does not keep pace with his companions, perhaps it is
because he hears a different drummer. Let him step to the
music which he hears, however measured or far away.
Direct Variation
A linear equation defined by the form y  kx (k  0).
k is the constant of variation (also known as the slope)
Ex1) Determine the direct variation
equation of the given graph.
Characteristics of Direct Variation:
Using a Table
Does y vary directly with x in the following examples?
(Check the ratio y/x)
Ex2)
x
-1
2
5
y
3
-6
15
Ex3)
x
7
9
-4
y
14
18
-8
Using Equations
Does y vary directly with x in the following equations?
(Can the equation be written in the form y = kx ?)
Ex4) 7 x  3 y  7
Ex5) 5 x  2 y
Perimeter
Ex6) The perimeter of a square varies directly as the length of
a side of the square.
a) Write a direct variation equation.
b) Find the constant of variation.
c) Find how long a side of the square must be for the perimeter
to be 64 cm.
Using Proportions
Ex7) Suppose y varies directly with x, and y = 15 when
x = 27. Find y when x = 18.
2.3: Direct Variation
HW: # 1-19 odd, 23, 24-27, 33, 34, 46, 47
Daniel, eh, son…. What does that sign say?!?!?