Chapter 4 Graphing

Graph of a Linear Function

Linear Function Fencing Company:

Fixed Charge for a Chain Link Fence Project $125

The rest of the cost for a 4 ft high fence is based on $8.50 per lineal foot of fencing.

A 6 ft high fence would be based on $13.00/ft

Cost = $125 + $8.50(Length)

Cost = $125 + $13.00(Length)

Pricing Graph for Chain Link Fence Projects

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 100 200 300

Length of Fencing Req'd (ft)

Co

st (

$)

6 ft Fence

4 ft Fence

Cost = $125 + $8.50(Length)

Cost = $125 + $13.00(Length)

Slope

Slope – a ratio that describes the steepness of a line and the direction that it slants.

y

xrun

rise

rise

run

2

33 units

2 units

Slope – a ratio that describes the steepness of a line and the direction that it slants.

y

x

Slope is relatively small & positive.

Slope is relatively large & positive.

Slope is relatively “small” & negative.

Slope is relatively “large” & negative.

4

1

1

3

5

11

2

Slope

Compute Slope when two points are known.

Slope formula:

12

12

xx

yy

run

risem

11, yx

22 , yx

rise

run

Compute the slope of this line.

12

12

xx

yym

y

x 0,3

4,4

4 – 0

4 – 3 1

4

0 – 4

3 – 4 1

4

1

4

Compute Slope

Compute Slope

Compute the slope of this line.

12

12

xx

yym

y

x 1,1

4,24 – (-1)

-2 – 1 3

5

-1 – 4

1 – (-2) 3

5

Compute Slope

Compute the slope of a line that passes through these two points. (-2,3) and (-6,5)

12

12

xx

yym

12 xx

m

53

-

-6-2

-

m

)2(6

35

m 4

2

m

2

1m

Horizontal Lines

Compute the slope of this line.

12

12

xx

yym

y

x

2,3

2,52 – 2

5 – (- 3) 8

0

y = 2

= 0

Vertical Lines Compute the slope of

this line.

12

12

xx

yym

y

x

3 ,4

5 ,4

5 – (- 3)

4 - 4 0

8

x = 4

= Undefined

Summary

Horizontal lines: Slope = 0

Vertical lines: Slope = Undefined

run

rise 0

run

rise

0

Use Intercepts to Graph Lines

Intercepts

Intercepts – locations where a graph intersects with an axis.

x

y

y - intercept

x - intercept

(0,5)

(-6,0)

x

y

y - intercept

x - intercept

(0,10)

(8,0)

Matching Excercise

Intercepts

Graph with Intercepts

Graph using intercepts. 3x + 2y = 12

In every x-intercept, y = 0

3x + 2(0) = 12

3x = 12

x = 4

(4,0)

Graph with Intercepts

Graph using intercepts. 3x + 2y = 12

In every y-intercept, x = 0

3(0) + 2y = 12

2y = 12

y = 6

(0,6)

(4,0)

Compute Intercepts

Compute the x and y intercepts of this equation. 4x – 3y = 24

x – intercept

(x, 0)

4x – 3(0) = 24

4x = 24x = 6

( 6,0 )

y – intercept

(0, y)

4(0) – 3y = 24

-3y = 24y = -8

( 0,-8 )

Slope Intercept Form

Graph the line that passes through the point (0,2) and has a slope of m =

Introduction 1 of 2

y

x

4

3 (0,2)

3 ↑

4 →

y-intercept

Introduction 2 of 2

Graph the line that passes through the point (0,-1) and has a slope of m =

y

x

3

2

(0,-1)

-2 ↓

3 →

y-intercept

Slope-Intercept Form

Equations like these…

…are in slope-intercept format.

53 xy

24

1 xy

63

2 xy

bmxy

Slope-Intercept Form bmxy

slope4

1

y-intercept = (0,2)

1

4

y-intercept

24

1 xy

Slope-Intercept Form

53 xy

bmxy

53 xy

slope = 31

3

y-intercept = (0,-5)

3

1

y-intercept

63

2 xy

Slope-Intercept Formbmxy

slope3

2

y-intercept = (0,-6)

-2

3

y-intercept

63

2

xy

Rewrite Linear Equations into Slope-Intercept Form

2x + y = 1

Rearranging Equations to Slope-Intercept Form bmxy

-2x -2x

y = -2x + 1

2x + y = 1

bmxy Rearranging Equations to Slope-Intercept Form

2x + 3y = 9-2x -2x

3y = -2x + 93 3 3

33

2

xy

2x + 3y = 9

x – 4y = 12

bmxy Rearranging Equations to Slope-Intercept Form

-x -x

-4y = -x + 12-4 -4 -4

34

1 xy

x – 4y = 12

Homework

Textbook Page 221 1-25 odd