Transcript

4.4 – Parallel & Perpendicular Lines

• Parallel Lines

• Parallel Lines – slopes are the same

• Parallel Lines – slopes are the same (m)

• Parallel Lines – slopes are the same (m)

• Perpendicular Lines

• Parallel Lines – slopes are the same (m)

• Perpendicular Lines – slopes are the opposite reciprical

• Parallel Lines – slopes are the same (m)

• Perpendicular Lines – slopes are the opposite reciprical

• Parallel Lines – slopes are the same (m)

• Perpendicular Lines – slopes are the opposite reciprical -m

• Parallel Lines – slopes are the same (m)

• Perpendicular Lines – slopes are the opposite reciprical -m

• Parallel Lines – slopes are the same (m)

• Perpendicular Lines – slopes are the opposite reciprical -1

m

• Parallel Lines – slopes are the same (m)

• Perpendicular Lines – slopes are the opposite reciprical -1

m

Ex. 1 Perpendicular or Parallel?

• Parallel Lines – slopes are the same (m)

• Perpendicular Lines – slopes are the opposite reciprical -1

m

Ex. 1 Perpendicular or Parallel?

a) y = ½x + 2

y = ½x – 9

• Parallel Lines – slopes are the same (m)

• Perpendicular Lines – slopes are the opposite reciprical -1

m

Ex. 1 Perpendicular or Parallel?

a) y = ½x + 2 ||

y = ½x – 9

• Parallel Lines – slopes are the same (m)

• Perpendicular Lines – slopes are the opposite reciprical -1

m

Ex. 1 Perpendicular or Parallel?

a) y = ½x + 2 || b) y = 3x – 5

y = ½x – 9 y = -⅓x + 7

• Parallel Lines – slopes are the same (m)• Perpendicular Lines – slopes are the

opposite reciprical -1

m

Ex. 1 Perpendicular or Parallel?

a) y = ½x + 2 || b) y = 3x – 5 _|_

y = ½x – 9 y = -⅓x + 7

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

y – y1 = m(x – x1)

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

y – y1 = m(x – x1)

y –

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

y – y1 = m(x – x1)

y –

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

y – y1 = m(x – x1)

y –

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

y – y1 = m(x – x1)

y – (-2) =

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

y – y1 = m(x – x1)

y – (-2) =

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

y – y1 = m(x – x1)

y – (-2) =

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

y – y1 = m(x – x1)

y – (-2) = 4(x -

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

y – y1 = m(x – x1)

y – (-2) = 4(x -

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

y – y1 = m(x – x1)

y – (-2) = 4(x -

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

y – y1 = m(x – x1)

y – (-2) = 4(x – (-3))

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

y – y1 = m(x – x1)

y – (-2) = 4(x – (-3))

y + 2 = 4(x + 3)

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

y – y1 = m(x – x1)

y – (-2) = 4(x – (-3))

y + 2 = 4(x + 3)

y + 2 = 4x + 12

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

y – y1 = m(x – x1)

y – (-2) = 4(x – (-3))

y + 2 = 4(x + 3)

y + 2 = 4x + 12

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

y – y1 = m(x – x1)

y – (-2) = 4(x – (-3))

y + 2 = 4(x + 3)

y + 2 = 4x + 12

- 2 - 2

Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

1) Find the slope needed.

x + 4y = 12

-x -x

4y = -x + 12

4 4 4

y = -¼x + 3

m = -¼, m┴ = 4

2) Use coordinate point & slope to write equation.

y – y1 = m(x – x1)

y – (-2) = 4(x – (-3))

y + 2 = 4(x + 3)

y + 2 = 4x + 12

- 2 - 2

y = 4x + 10

Ex. 3 Write the slope-intercept form of the equation through (9, 0) parallel to the graph of y = -⅓x + 2.

Ex. 3 Write the slope-intercept form of the equation through (9, 0) parallel to the graph of y = -⅓x + 2.

1) Find the slope needed.

y = -⅓x + 2

m = -⅓, m|| = -⅓

Ex. 3 Write the slope-intercept form of the equation through (9, 0) parallel to the graph of y = -⅓x + 2.

1) Find the slope needed.

y = -⅓x + 2

m = -⅓, m|| = -⅓

2) Use coordinate point & slope to write equation.

y – y1 = m(x – x1)

y – (0) = -⅓(x – (9))

y = -⅓(x – 9)

y = -⅓ x + 3


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