Algebra 2/Trig
Name: ____________________________________
Lesson 1.4: Direct Variation and Proportion p. 29
DIRECT VARIATION
The variable ___ varies directly as ___ if there is a nonzero constant k such that y = kx.
The equation y = kx is called a direct-variation equation and the number k is called the
___________________ of variation. The y-intercept is ____ so the graph passes through the origin.
SO…
y = kx is the equation of direct-variation.
y varies directly as x (if x goes up, y goes up, if x goes down, y goes down)
k is the constant of variation
How do we find k? If y = kx
Example 1:
Given a table of values determine if the table represents direct variation. If it does, the ratio of
If the table does represent direct variation, write the equation of direct variation.
x y
1 3
3 9
5 15
7 21
Example 2:
If y varies directly as x, and x = -3 when y = 12,
Find:
a. the constant of variation (k)
b. the equation of variation
c. y when x = 19.
Is there another way to find y when x = 19?
y
is a constant (k).
x
PROPORTION OR CROSS PRODUCT:
For b ≠ 0 and d ≠ 0:
If
a c
 , then ad  bc .
b d
Example 3:
Solve:
x7
x

8
5
______________________________________________________________________________________________
HW: pages 33 – 36 #15 – 57 (3rds), and 66 – 70 all. Write out problem, show work.