Intermediate Algebra (11th edition)

3.3 Linear Equations in Two Variables

Slope-Intercept Form

Point-Slope Form

Standard Form

Horizontal Line

Vertical Line
xa

yb

AxByC

yy 1 m 1 xx 12

ymxb y-intercept is.

is on the line,

Standard form

Horizontal line

x=- 1 Vertical line

y= 4

2 x- 5 y= 8

y- 3 = 41 x- 52 1 5, 3 2 m=4.

y= 2 x+ 3 m=2, 1 0, 3 2

CONCEPTS EXAMPLES

CHAPTER 3 Summary 201

3.5 Introduction to Relations and

Functions

A functionis a set of ordered pairs such that, for each first
component, there is one and only one second component.
The set of first components is called the domain,and the
set of second components is called the range.

defines a function ƒ with domain, the

set of x-values, and range, the set of y-values,

y=x^2 defines a function with domain 1 - q, q 2 and range 3 0, q 2.

5 - 1, 0, 1 6 5 4, 6 6.

ƒ= 51 - 1, 4 2 , 1 0, 6 2 , 1 1, 4 26

3.4 Linear Inequalities in Two Variables

Graphing a Linear Inequality

Step 1 Draw the graph of the line that is the boundary.
Make the line solid if the inequality involves
or. Make the line dashed if the inequality
involves or

Step 2 Choose any point not on the line as a test point.
Substitute the coordinates into the inequality.

Step 3 Shade the region that includes the test point if
the test point satisfies the original inequality.
Otherwise, shade the region on the other side of
the boundary line.

6 7.

Ú

...

Graph

Draw the graph of Use a solid line because of the

inclusion of equality in the symbol

Choose , for example.

True

Shade the side of the line that includes

1 0, 0 2.

0 ... 6

2102 - 3102 ...

?

6

10 , 02

....

2 x- 3 y=6.

2 x- 3 y...6.

y

(0, 0) 0 3 x

 2

3.6 Function Notation and Linear

Functions

To evaluate a function ƒ, where defines the range
value for a given value of xin the domain, substitute the
value wherever xappears.

To write an equation that defines a function ƒ in function
notation, follow these steps.

Step 1 Solve the equation for y.

Step 2 Replace ywith ƒ 1 x 2.

ƒ 1 x 2 If then

Write using notation for a function ƒ.

Subtract 2x.

Divide by 3.

ƒ 1 x 2 =- y=ƒ 1 x 2

2

3

x+ 4

y=-

2

3

x+ 4

3 y=- 2 x+ 12

2 x+ 3 y= 12

ƒ 112 = 12 - 7112 + 12 =6.

ƒ 1 x 2 =x^2 - 7 x+12,