Section 2-3: Direct Variation
Writing and Interpreting a Direct Variation
direct variation--a linear function defined by an equation of the form y=kx, where
k=0
constant of variation--
passes through the origin!!! (0, 0)
Example 1
For each function, determine whether y varies directly with x. If so, find the constant of
variation and write the equation.
Example 2
For each function, determine whether y varies directly with x. If so, find the constant of
variation.
Example 3
A dripping faucet wastes a cup of water if it drips for three minutes. The amount of water
wasted varies directly with the amount of time the faucet drips.
a) Find the constant of variation k and write an equation to model the direct variation.
b) Find how long the faucet must drip to waste 4 1/2 cups of water.
Quick Check 3
The circumference of a circle varies directly with the diameter of the circle. The
formula
relates the circumference to the diameter.
a) What is the constant of variation?
b) Find the diameter of a circle with circumference 105 cm to the nearest tenth.
Can use proportions to solve some direct variations!
Example 4
Suppose y varies directly with x, and x=27 when y=-51. Find x when y=-17.
Assignment: 2-3 Worksheet #1-7, 12, 13, 16, 17, 20, 21, 24, 25, 28, 29
and GPS Worksheet