chapter 4 graphing graph of a linear function. linear function fencing company: fixed charge for a...
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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