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4.4 – Parallel & Perpendicular Lines

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Parallel Lines

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Parallel Lines – slopes are the same

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Parallel Lines – slopes are the same (m)

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Perpendicular Lines

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Parallel Lines – slopes are the same (m) Perpendicular Lines – slopes are the opposite reciprical

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Parallel Lines – slopes are the same (m) Perpendicular Lines – slopes are the opposite reciprical

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Parallel Lines – slopes are the same (m) Perpendicular Lines – slopes are the opposite reciprical -m

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Parallel Lines – slopes are the same (m) Perpendicular Lines – slopes are the opposite reciprical -m

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Parallel Lines – slopes are the same (m) Perpendicular Lines – slopes are the opposite reciprical -1 m

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Parallel Lines – slopes are the same (m) Perpendicular Lines – slopes are the opposite reciprical -1 m Ex. 1 Perpendicular or Parallel?

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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

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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

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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

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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

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

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1)Find the slope needed.

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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.

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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

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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

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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

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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

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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

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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

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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

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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.

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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.

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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.

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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 – y 1 = m(x – x 1 )

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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 – y 1 = m(x – x 1 ) y –

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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 – y 1 = m(x – x 1 ) y –

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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 – y 1 = m(x – x 1 ) y –

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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 – y 1 = m(x – x 1 ) y – (-2) =

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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 – y 1 = m(x – x 1 ) y – (-2) =

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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 – y 1 = m(x – x 1 ) y – (-2) =

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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 – y 1 = m(x – x 1 ) y – (-2) = 4(x -

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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 – y 1 = m(x – x 1 ) y – (-2) = 4(x -

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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 – y 1 = m(x – x 1 ) y – (-2) = 4(x -

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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 – y 1 = m(x – x 1 ) y – (-2) = 4(x – (-3))

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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 – y 1 = m(x – x 1 ) y – (-2) = 4(x – (-3)) y + 2 = 4(x + 3)

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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 – y 1 = m(x – x 1 ) y – (-2) = 4(x – (-3)) y + 2 = 4(x + 3) y + 2 = 4x + 12

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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 – y 1 = m(x – x 1 ) y – (-2) = 4(x – (-3)) y + 2 = 4(x + 3) y + 2 = 4x + 12

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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 – y 1 = m(x – x 1 ) y – (-2) = 4(x – (-3)) y + 2 = 4(x + 3) y + 2 = 4x + 12 - 2 - 2

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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 – y 1 = m(x – x 1 ) y – (-2) = 4(x – (-3)) y + 2 = 4(x + 3) y + 2 = 4x + 12 - 2 - 2 y = 4x + 10

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

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1) Find the slope needed. y = -⅓x + 2 m = -⅓, m || = -⅓

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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 – y 1 = m(x – x 1 ) y – (0) = -⅓ (x – (9)) y = -⅓ (x – 9) y = -⅓ x + 3

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