Page 126 - Math Course 3 (Book 1)

Direct Variation Equation
Mo. 4

Lesson 2 parent graph
The parent graph is the simplest graph in a family.

KEY CONCEPTS: y = x + b, y =x
1. Write and graph direct variation equations. y = 2x + b
2. Write and solve direct variation equations. y = x – b, y = x + 2
3. Solve problems involving direct variation. y = x

y = x is the simplest y = x – 2
MO. 4 - L2a graph so it is the
parent graph
Write and Graph Direct
Variation

Vocabulary A-Z Concept Summary

Let us learn some vocabulary Direct Variation Graphs

Words
Direct variation equations are of the form y = kx,
direction variation where k ≠ 0
is described by an equation of the form y = kx, The graph y = kx always passes through the origin.
where k ≠ 0.
The slope is The slope is
positive if k > 0 negative if k < 0.
constant of variation y y

The equation y = kx represents a constant rate of y = kx
change and k is the constant of variation.
0
y Variables Directly with x y = kx x 0 x
y = 4 when x = 2

Find y when x = 4
y = kx

y = k • 2 y = 2x Let’s Begin
k = 2 y = 2 • 4

family of graphs
includes graphs and equations of graphs that have Slope and Constant of Variation
at least one characteristic in common.
Example
y = x + b, y =x
y = 2x + b
y = x – b, Name the constant
y = x y = x + 2 of variation for the
equation. Then find the
slope of the line that
y = x – 2 passes through the pair
of points.

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