This document provides an overview of direct variation graphs and equations. It defines direct variation as two quantities where y=kx, with k being a constant coefficient. Direct variation graphs are characterized as (1) having a slope of k and (2) passing through the origin. Several examples are worked through, showing how to write direct variation equations from values and graph the equations. Key characteristics of direct variations are reviewed, including the linear equation form y=kx, a line graph with slope that passes through the origin, and tables where y-values change constantly as x-values change. Homework problems are assigned from the textbook.

1. Lesson 4.5 1st.notebook November 22, 2010
Characteristics of direct variation graphs.
Lesson 4.5: Direct Variation
Two variables x and y vary directly if there is a 1. the line has a slope of "k".
nonzero number k such that the following is true. AND
y = kx direct variation model 2. the line passes through the origin, because the "b"
is 0, and thus, the y­intercept point is the origin..
The number k is constant of variation (or slope)
although k is technically a coefficient of x.
The k coefficient corresponds with slope in "y = mx +
b" but the b is understood to be zero.
The two quantities (x and y) that vary directly are said
to have a direct variation between them.
Nov 15­3:33 PM Nov 15­3:43 PM
Example 1
Find the constant of variation, k, and the slope for each
direct variation example. Then graph each equation. Example 2:
a. y = 2x b. y = ­1 x The quantities x and y vary directly
2 with x = ­3 and y = ­30.
a. Write an equation that relates
x and y (y = kx).
b. Find the value of y when x = 8.
Nov 15­3:47 PM Nov 15­3:50 PM
Example 3:
The quantities x and y vary directly Lesson 4.5 Part II:
with x = 5 and y = 20. Use a Ratio to Model Direct Variation
a. Write an equation that relates
x and y (y = kx). Solve y = kx for k.
b. Find the value of y when x = 10.
y = k x
x x
y = k Ratio form for
direct variation
x
Nov 15­3:52 PM Nov 15­3:55 PM
1

2. Lesson 4.5 1st.notebook November 22, 2010
Review:
Direct Variations are linear functions that meet
extra conditions.
I. Equation: y = kx (or y = mx + 0) form.
The m or k must be a positive or negative.
II. Graph: A line with a positive or negative slope,
and the line crosses the y­axis at (0, 0) the origin.
III. Table: If x­values are selected so as to change
constantly by 1, then the y­values will change
constantly by an amount called k (or m).
x | ­2 | ­1 | 0 | 1 | 2 |
y |­10 ­5 0 5 10
y = 5x
Nov 15­4:06 PM Nov 15­8:31 PM
Homework: p. 237
(1­14, 16 ­ 20 even, 21­23, 28, 30)
Nov 15­4:08 PM
2