4.4 – Parallel & Perpendicular Lines. Parallel Lines.

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Presentation transcript:

4.4 – Parallel & Perpendicular Lines

Parallel Lines

Parallel Lines – slopes are the same

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.

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

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 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 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 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 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 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 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 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 )

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 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) 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 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) 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 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) 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 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) 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 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) 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 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) 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 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 -

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 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 -

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 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 -

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 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))

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 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)

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 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

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 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

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 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

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 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 y = 4x + 10

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