Page 378 - Algebra 1

Solving y = kx for k gives a ratio for the constant of variation in a direct variation.
y = kx = kx
_y _ xx
Divide both sides by x (x ≠ 0).
Another way to decide if a relationship is a direct variation is to check whether the ratio _y is the same for each ordered pair (except where x = 0).
Identifying Direct Variation from Ordered Pairs
Tell whether the set of ordered pairs represents a direct variation.
a. (2, -14), (5, -35), (-3, 21)
SOLUTION
Find the ratio _y for each ordered pair. x
_y = k x
x
Example
2
-14
__ = -7
-35
21
__ = -7
__ = -7
2 5 -3
The ordered pairs represent a direct variation because the ratio _y is the x
same for each ordered pair.
b. (2, 4), (3, 5), (5, 7)
SOLUTION
Find the ratio _y for each ordered pair. x
_5 = _5 _7 = _7 23355
_4 = 2
The ordered pairs do not represent a direction variation because the ratio _y
is not the same for each ordered pair.
To write an equation for a direct variation, one point other than the origin that lies on the graph of the equation is needed. First find the constant of variation, k, and then use the value of k to write an equation.
Writing an Equation Given a Point
Write an equation for a direct variation that includes the point (6, 24).
x
Example
3
SOLUTION
y = kx 24 = k · 6
4=k y = 4x
Begin with the equation for a direct variation. Substitute the x- and y-values from the point. Divide both sides by 6 to solve for k.
Write the direct variation equation and include the constant of variation, k.
Lesson 56 363