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2
TEKS
TEKS
TEKS
Big Idea 1
2A.1.A
Big Idea 2
2A.4.A
Big Idea 3
a.3
CHAPTER SUMMARY
SUMMARY
SUMMARY
SUMMARY
SUMMARY
SUMMARY
SUMMARY
140 Chapter 2 Linear Equations and Functions
BIG IDEAS For Your Notebook
Representing Relations and Functions
A relation pairs input values with output values. A relation is a function if each
input value is paired with exactly one output value.
This relation is a function because each This relation is not a function because
input has exactly one output. a vertical line intersects the graph at
more than one point.
Graphing Linear Equations and Inequalities in Two Variables
Linear Function Direct Variation Absolute Value Linear Inequality
Equation Function
y
(0, b)
slope 5 m
Input Output
24
22
0
2
4
x
0
4
6
y
(0, 0)
x
y
x
(h, k)
y 5 mx 1 b y 5 ax y 5 a⏐x 2 h⏐ 1 k Ax 1 By > C
Writing Linear Equations and Inequalities in Two Variables
Form Equation Key Facts
Slope-intercept form y 5 mx 1 b The graph is a line with slope m and
y-intercept b.
Standard form Ax 1 By 5 C The graph is a line with intercepts
x 5 C } and y 5
A C } .
B
Point-slope form y 2 y 1 5 m(x 2 x 1 ) The graph is a line that has slope m
and passes through (x 1 , y 1 ).
Direct variation y 5 ax, a Þ 0 The graph is a line that passes
through the origin and has slope a
(the constant of variation).
Linear inequality Ax 1 By > C The graph is a half-plane with
boundary line Ax 1 By 5 C.
1
y
1
Algebra
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Electronic Function Library
x
y
x