geometry section 3-4 1112

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?

VOCABULARY

1. Slope-intercept Form:

2. Point-slope form:

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:

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

EXAMPLE 1

Identify the slope and y-intercept for each line and graph the lines.

a. y =

EXAMPLE 1

a. y =

EXAMPLE 1

a. y =

EXAMPLE 1

a. y =

b = 0y-intercept: (0, 0)

EXAMPLE 1

a. y =

EXAMPLE 1

a. y =

EXAMPLE 1

a. y =

EXAMPLE 1

a. y =

EXAMPLE 1

a. y =

EXAMPLE 1

a. y =

EXAMPLE 1

a. y =

EXAMPLE 1

a. y =

EXAMPLE 1

b. 2y − x = −6

EXAMPLE 1

b. 2y − x = −6 +x

EXAMPLE 1

b. 2y − x = −6 +x +x

EXAMPLE 1

b. 2y − x = −6 +x +x

EXAMPLE 1

b. 2y − x = −6 +x +x

2y = x − 6

EXAMPLE 1

b. 2y − x = −6 +x +x

2y = x − 62 2

EXAMPLE 1

b. 2y − x = −6 +x +x

2y = x − 62 2

x − 3

EXAMPLE 1

b. 2y − x = −6 +x +x

2y = x − 62 2

x − 3

EXAMPLE 1

b. 2y − x = −6 +x +x

2y = x − 62 2

x − 3

y-intercept = (0, -3)

EXAMPLE 1

b. 2y − x = −6 +x +x

2y = x − 62 2

x − 3

EXAMPLE 1

b. 2y − x = −6 +x +x

2y = x − 62 2

x − 3

EXAMPLE 1

b. 2y − x = −6 +x +x

2y = x − 62 2

x − 3

EXAMPLE 1

b. 2y − x = −6 +x +x

2y = x − 62 2

x − 3

EXAMPLE 1

b. 2y − x = −6 +x +x

2y = x − 62 2

x − 3

EXAMPLE 1

b. 2y − x = −6 +x +x

2y = x − 62 2

x − 3

EXAMPLE 1

b. 2y − x = −6 +x +x

2y = x − 62 2

x − 3

EXAMPLE 1

b. 2y − x = −6 +x +x

2y = x − 62 2

x − 3

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)

EXAMPLE 2

graph the line.

a. m = -2, (0, 4)

Use slope-intercept

EXAMPLE 2

graph the line.

a. m = -2, (0, 4)

Use slope-intercept

y = mx + b

EXAMPLE 2

graph the line.

a. m = -2, (0, 4)

Use slope-intercept

y = mx + b

y = −2x + 4

EXAMPLE 2

graph the line.

a. m = -2, (0, 4)

Use slope-intercept

y = mx + b

y = −2x + 4

EXAMPLE 2

graph the line.

a. m = -2, (0, 4)

Use slope-intercept

y = mx + b

y = −2x + 4

EXAMPLE 2

graph the line.

a. m = -2, (0, 4)

Use slope-intercept

y = mx + b

y = −2x + 4

EXAMPLE 2

graph the line.

a. m = -2, (0, 4)

Use slope-intercept

y = mx + b

y = −2x + 4

EXAMPLE 2

graph the line.

a. m = -2, (0, 4)

Use slope-intercept

y = mx + b

y = −2x + 4

EXAMPLE 2

graph the line.

a. m = -2, (0, 4)

Use slope-intercept

y = mx + b

y = −2x + 4

EXAMPLE 2

graph the line.

a. m = -2, (0, 4)

Use slope-intercept

y = mx + b

y = −2x + 4

EXAMPLE 2

graph the line.

a. m = -2, (0, 4)

Use slope-intercept

y = mx + b

y = −2x + 4

EXAMPLE 2

graph the line.b. m = 3/4, (8, -2)

EXAMPLE 2

Use point-slope

EXAMPLE 2

Use point-slope

y − y

1= m(x − x

EXAMPLE 2

Use point-slope

y − y

1= m(x − x

y + 2 = 3

4(x − 8)

EXAMPLE 2

Use point-slope

y − y

1= m(x − x

y + 2 = 3

4(x − 8)

y + 2 = 3

4x − 6

EXAMPLE 2

Use point-slope

y − y

1= m(x − x

y + 2 = 3

4(x − 8)

y + 2 = 3

4x − 6

4x − 8

EXAMPLE 2

Use point-slope

y − y

1= m(x − x

y + 2 = 3

4(x − 8)

y + 2 = 3

4x − 6

4x − 8

EXAMPLE 2

Use point-slope

y − y

1= m(x − x

y + 2 = 3

4(x − 8)

y + 2 = 3

4x − 6

4x − 8

EXAMPLE 2

Use point-slope

y − y

1= m(x − x

y + 2 = 3

4(x − 8)

y + 2 = 3

4x − 6

4x − 8

EXAMPLE 2

Use point-slope

y − y

1= m(x − x

y + 2 = 3

4(x − 8)

y + 2 = 3

4x − 6

4x − 8

EXAMPLE 3

Write the equation for the line.

EXAMPLE 3

m = −

EXAMPLE 3

m = −

(4, -1)

EXAMPLE 3

m = −

(4, -1)

y − y

1= m(x − x

EXAMPLE 3

m = −

(4, -1)

y − y

1= m(x − x

y +1= − 5

7(x − 4)

EXAMPLE 3

m = −

(4, -1)

y − y

1= m(x − x

y +1= − 5

7(x − 4)

y +1= − 5

7x + 20

EXAMPLE 3

m = −

(4, -1)

y − y

1= m(x − x

y +1= − 5

7(x − 4)

y +1= − 5

7x + 20

y = − 5

7x + 13

EXAMPLE 3

(3, 2) =

EXAMPLE 3

(3, 2)

y − y

1= m(x − x

EXAMPLE 3

(3, 2)

y − y

1= m(x − x

y − 2 = 3

4(x − 3)

EXAMPLE 3

(3, 2)

y − y

1= m(x − x

y − 2 = 3

4(x − 3)

y − 2 = 3

4x − 9

EXAMPLE 3

(3, 2)

y − y

1= m(x − x

y − 2 = 3

4(x − 3)

4x − 1

y − 2 = 3

4x − 9

CHECK YOUR UNDERSTANDING

Review problems #1-12 on p. 200

PROBLEM SET

p. 200 #13-41 odd, 55

“We can have facts without thinking, but we cannot have thinking without facts.” - John Dewey

geometry section 3-4 1112

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