Name:____________________________
Date: ________________
Binder Notes
Lesson 3-4
Direct Variation
pages 182-184
A direct variation is described by the equation y = kx, where k  0. Direct
variation represents a start value of (0, 0) and a constant rate of change. This
constant rate of change is described by the variable k and called the constant
of variation.
What is the relationship between the constant of variation (k) and the slope of a line?
(2, 4)
y = 2x
k = ___ = ____
slope =
(0, 0)
In a direct variation equation y = kx:
 The slope of the graph is ______.
 The x-intercept is _______.
 The y-intercept is _______.
To graph a direct variation equation y = kx:
1.) Write ___ as a ratio.
2.) Graph _______.
𝒓𝒊𝒔𝒆
3.) Use the slope (
𝒓𝒖𝒏
) to generate more points.
4.) Draw a line through the points.
1
1
1. Graph y = -4x.
2. Graph y = x.
3
To write a direct variation equation y = kx:
1.) Substitute values for ___ and ____ into y = kx.
2.) Solve for ______.
3.) Rewrite y = kx with the value for ____.
3. Suppose y varies directly as x, and y = 9 when x = -3.
a.) Write a direct variation equation that relates x and y.
b.) Use the equation to find the value x when y = 15.
2
A real-world application of direct variation is the distance formula.
The Distance Formula
Distance = rate  time
d = rt
4. The Knable family is driving cross-country on vacation. They drive 330 miles in
5.5 hours.
a.) Write a direct variation equation to find the distance d driven in time t.
b.) Graph the equation.
c.) Estimate how many hours it would take to drive 500 miles.
3