Algebra 1 Notes SOL A.8 Direct Variation Mrs. Grieser
Key Concepts of Direct Variation
y = kx, where k = constant of variation
k is the slope of the graph of the line (k = m), and k =
x
y
The line always goes through the origin (since the y-intercept is always 0)
Name: _____________________________________________ Date: _____________ Block: _______
Direct Variation
When two things are related in such a way that the ratio of their values always remains
the same, the two variables are said to be in direct variation.
Direct variations are directly proportional.
Direct Variation
Two variables show direct variation when they can be modeled by
the equation y = kx, where k 0.
Constant of
Variation
The constant “k” in y = kx is called the constant of variation.
Example of Direct Variation:
Suppose an object on Earth weighs 150 pounds. On Neptune, the same object would weigh
165 pounds. We determine the weight on Neptune as compared to that on Earth by
multiplying the object’s weight on Earth by ____________. (how do we find this??)
The weights on Earth and Neptune vary directly, and the constant of variation is 1.1.
So: y = 1.1x, where x represents the weight on Earth, and y represents the weight on
Neptune.
Graphing Direct Variations
Use y = mx + b.
In direct variation equations, m = k, the constant of
variation, and b = 0.
Direct variations ALWAYS go through the origin (0, 0)
Identifying Direct Variation Equations
If a linear equation can be written in the form y = kx, then we have direct variation.
Convert equation to function form (solve for y) to put in slope-intercept form (y = mx + b)
If b = 0 (y-intercept = 0), then we have a direct variation.
Do the following equations show direct variation? If so, what is the constant of variation?
a) y = 4x + 2
b = _______
Direct
variation?______
If so, k = _______
b) 2x – 3y = 0
Put in function form:
___________
b = ____
Direct variation? ______
k = _______
c) -x + y = 1
d) 4x – 5y = 0
