Algebra 1 Unit 3 Lesson 3: Direct Variation
A direct variation is described by an equation of the form y  kx , where k  0 . The equation y  kx
illustrates a constant rate of change, and k is the constant of variation, also called the constant of
proportionality.
Example
1)
You Try
The constant of variation is _____
The constant of variation is _____
2) Graph y 
3
x
4
y  5 x
3) Suppose y varies directly as x, and y=72 when
x = 8.
a) Write a direct variation equation that relates x
and y.
Suppose y varies directly as x, and y=98 when
x = 14.
a) Write a direct variation equation that relates x
and y.
b) Use the direct variation equation to find x when
y=63.
b) Use the direct variation equation to find y when
x=-4.
4) The distance a jet travels varies directly as the number of hours it flies. A jet traveled 3,420 miles in 6
hours.
a) Write a direct variation equation for the distance d flown in time t.
b) Graph the equation
c) Estimate how many hours it will take for an airliner to fly 6,500 miles.
________________________________________________________________________________________________________________________
You Try: A hot-air balloon’s height varies directly as the balloon’s ascent time in minutes. The hot air
balloon rose 350ft in 5 minutes.
a) Write a direct variation for the distance d ascended in time t.
b) Graph the equation.
c) Estimate how many minutes it would take to ascend 2100 feet.
d) About how many minutes would it take to ascend 3500 feet?