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Equations of Lines
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SECTION 3-4Equations of Lines
Tuesday, January 3, 2012
ESSENTIAL QUESTIONS
How do you write an equation of a line given information about the graph?
How do you solve problems by writing equations?
Tuesday, January 3, 2012
VOCABULARY
1. Slope-intercept Form:
2. Point-slope form:
Tuesday, January 3, 2012
VOCABULARY
1. Slope-intercept Form: y = mx + b, where m = slope and b = y coordinate of the y-intercept -- (0, b)
2. Point-slope form:
Tuesday, January 3, 2012
VOCABULARY
1. Slope-intercept Form: y = mx + b, where m = slope and b = y coordinate of the y-intercept -- (0, b)
2. Point-slope form: y - y1 = m(x - x1), where m = slope and (x1, y1) is a point on the line
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
a. y =
12
x
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
a. y =
12
x
m =
12
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
a. y =
12
x
m =
12
b = 0
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
a. y =
12
x
m =
12
b = 0y-intercept: (0, 0)
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
a. y =
12
x
m =
12
b = 0y-intercept: (0, 0)
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
a. y =
12
x
m =
12
b = 0y-intercept: (0, 0)
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
a. y =
12
x
m =
12
b = 0y-intercept: (0, 0)
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
a. y =
12
x
m =
12
b = 0y-intercept: (0, 0)
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
a. y =
12
x
m =
12
b = 0y-intercept: (0, 0)
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
a. y =
12
x
m =
12
b = 0y-intercept: (0, 0)
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
a. y =
12
x
m =
12
b = 0y-intercept: (0, 0)
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
a. y =
12
x
m =
12
b = 0y-intercept: (0, 0)
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
b. 2y − x = −6
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
b. 2y − x = −6 +x
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
b. 2y − x = −6 +x +x
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
b. 2y − x = −6 +x +x
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
b. 2y − x = −6 +x +x
2y = x − 6
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
b. 2y − x = −6 +x +x
2y = x − 62 2
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
b. 2y − x = −6 +x +x
2y = x − 62 2
y =
12
x − 3
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
b. 2y − x = −6 +x +x
2y = x − 62 2
y =
12
x − 3
m =
12
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
b. 2y − x = −6 +x +x
2y = x − 62 2
y =
12
x − 3
m =
12
y-intercept = (0, -3)
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
b. 2y − x = −6 +x +x
2y = x − 62 2
y =
12
x − 3
m =
12
y-intercept = (0, -3)
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
b. 2y − x = −6 +x +x
2y = x − 62 2
y =
12
x − 3
m =
12
y-intercept = (0, -3)
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
b. 2y − x = −6 +x +x
2y = x − 62 2
y =
12
x − 3
m =
12
y-intercept = (0, -3)
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
b. 2y − x = −6 +x +x
2y = x − 62 2
y =
12
x − 3
m =
12
y-intercept = (0, -3)
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
b. 2y − x = −6 +x +x
2y = x − 62 2
y =
12
x − 3
m =
12
y-intercept = (0, -3)
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
b. 2y − x = −6 +x +x
2y = x − 62 2
y =
12
x − 3
m =
12
y-intercept = (0, -3)
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
b. 2y − x = −6 +x +x
2y = x − 62 2
y =
12
x − 3
m =
12
y-intercept = (0, -3)
Tuesday, January 3, 2012
EXAMPLE 1
Identify the slope and y-intercept for each line and graph the lines.
b. 2y − x = −6 +x +x
2y = x − 62 2
y =
12
x − 3
m =
12
y-intercept = (0, -3)
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.
a. m = -2, (0, 4)
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.
a. m = -2, (0, 4)
Use slope-intercept
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.
a. m = -2, (0, 4)
Use slope-intercept
y = mx + b
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.
a. m = -2, (0, 4)
Use slope-intercept
y = mx + b
y = −2x + 4
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.
a. m = -2, (0, 4)
Use slope-intercept
y = mx + b
y = −2x + 4
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.
a. m = -2, (0, 4)
Use slope-intercept
y = mx + b
y = −2x + 4
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.
a. m = -2, (0, 4)
Use slope-intercept
y = mx + b
y = −2x + 4
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.
a. m = -2, (0, 4)
Use slope-intercept
y = mx + b
y = −2x + 4
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.
a. m = -2, (0, 4)
Use slope-intercept
y = mx + b
y = −2x + 4
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.
a. m = -2, (0, 4)
Use slope-intercept
y = mx + b
y = −2x + 4
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.
a. m = -2, (0, 4)
Use slope-intercept
y = mx + b
y = −2x + 4
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.
a. m = -2, (0, 4)
Use slope-intercept
y = mx + b
y = −2x + 4
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.b. m = 3/4, (8, -2)
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.b. m = 3/4, (8, -2)
Use point-slope
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.b. m = 3/4, (8, -2)
Use point-slope
y − y
1= m(x − x
1)
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.b. m = 3/4, (8, -2)
Use point-slope
y − y
1= m(x − x
1)
y + 2 = 3
4(x − 8)
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.b. m = 3/4, (8, -2)
Use point-slope
y − y
1= m(x − x
1)
y + 2 = 3
4(x − 8)
y + 2 = 3
4x − 6
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.b. m = 3/4, (8, -2)
Use point-slope
y − y
1= m(x − x
1)
y + 2 = 3
4(x − 8)
y + 2 = 3
4x − 6
y = 3
4x − 8
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.b. m = 3/4, (8, -2)
Use point-slope
y − y
1= m(x − x
1)
y + 2 = 3
4(x − 8)
y + 2 = 3
4x − 6
y = 3
4x − 8
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.b. m = 3/4, (8, -2)
Use point-slope
y − y
1= m(x − x
1)
y + 2 = 3
4(x − 8)
y + 2 = 3
4x − 6
y = 3
4x − 8
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.b. m = 3/4, (8, -2)
Use point-slope
y − y
1= m(x − x
1)
y + 2 = 3
4(x − 8)
y + 2 = 3
4x − 6
y = 3
4x − 8
Tuesday, January 3, 2012
EXAMPLE 2
Write the equation of the line, choosing which form you would need before you begin. Then
graph the line.b. m = 3/4, (8, -2)
Use point-slope
y − y
1= m(x − x
1)
y + 2 = 3
4(x − 8)
y + 2 = 3
4x − 6
y = 3
4x − 8
Tuesday, January 3, 2012
EXAMPLE 3
Write the equation for the line.
a.
Tuesday, January 3, 2012
EXAMPLE 3
Write the equation for the line.
a.
m = −
57
Tuesday, January 3, 2012
EXAMPLE 3
Write the equation for the line.
a.
m = −
57
(4, -1)
Tuesday, January 3, 2012
EXAMPLE 3
Write the equation for the line.
a.
m = −
57
(4, -1)
y − y
1= m(x − x
1)
Tuesday, January 3, 2012
EXAMPLE 3
Write the equation for the line.
a.
m = −
57
(4, -1)
y − y
1= m(x − x
1)
y +1= − 5
7(x − 4)
Tuesday, January 3, 2012
EXAMPLE 3
Write the equation for the line.
a.
m = −
57
(4, -1)
y − y
1= m(x − x
1)
y +1= − 5
7(x − 4)
y +1= − 5
7x + 20
7
Tuesday, January 3, 2012
EXAMPLE 3
Write the equation for the line.
a.
m = −
57
(4, -1)
y − y
1= m(x − x
1)
y +1= − 5
7(x − 4)
y +1= − 5
7x + 20
7
y = − 5
7x + 13
7
Tuesday, January 3, 2012
EXAMPLE 3
Write the equation for the line.
b.
Tuesday, January 3, 2012
EXAMPLE 3
Write the equation for the line.
b.
m =
68
Tuesday, January 3, 2012
EXAMPLE 3
Write the equation for the line.
b.
m =
68 =
34
Tuesday, January 3, 2012
EXAMPLE 3
Write the equation for the line.
b.
m =
68
(3, 2) =
34
Tuesday, January 3, 2012
EXAMPLE 3
Write the equation for the line.
b.
m =
68
(3, 2)
y − y
1= m(x − x
1)
=
34
Tuesday, January 3, 2012
EXAMPLE 3
Write the equation for the line.
b.
m =
68
(3, 2)
y − y
1= m(x − x
1)
y − 2 = 3
4(x − 3)
=
34
Tuesday, January 3, 2012
EXAMPLE 3
Write the equation for the line.
b.
m =
68
(3, 2)
y − y
1= m(x − x
1)
y − 2 = 3
4(x − 3)
=
34
y − 2 = 3
4x − 9
4
Tuesday, January 3, 2012
EXAMPLE 3
Write the equation for the line.
b.
m =
68
(3, 2)
y − y
1= m(x − x
1)
y − 2 = 3
4(x − 3)
y = 3
4x − 1
4
=
34
y − 2 = 3
4x − 9
4
Tuesday, January 3, 2012
CHECK YOUR UNDERSTANDING
Review problems #1-12 on p. 200
Tuesday, January 3, 2012
PROBLEM SET
Tuesday, January 3, 2012
PROBLEM SET
p. 200 #13-41 odd, 55
“We can have facts without thinking, but we cannot have thinking without facts.” - John Dewey
Tuesday, January 3, 2012
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