4.4 – Parallel & Perpendicular Lines. Parallel Lines.

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<ul><li> Slide 1 </li> <li> 4.4 Parallel &amp; Perpendicular Lines </li> <li> Slide 2 </li> <li> Parallel Lines </li> <li> Slide 3 </li> <li> Parallel Lines slopes are the same </li> <li> Slide 4 </li> <li> Parallel Lines slopes are the same (m) </li> <li> Slide 5 </li> <li> Perpendicular Lines </li> <li> Slide 6 </li> <li> Parallel Lines slopes are the same (m) Perpendicular Lines slopes are the opposite reciprical </li> <li> Slide 7 </li> <li> Parallel Lines slopes are the same (m) Perpendicular Lines slopes are the opposite reciprical </li> <li> Slide 8 </li> <li> Parallel Lines slopes are the same (m) Perpendicular Lines slopes are the opposite reciprical -m </li> <li> Slide 9 </li> <li> Parallel Lines slopes are the same (m) Perpendicular Lines slopes are the opposite reciprical -m </li> <li> Slide 10 </li> <li> Parallel Lines slopes are the same (m) Perpendicular Lines slopes are the opposite reciprical -1 m </li> <li> Slide 11 </li> <li> Parallel Lines slopes are the same (m) Perpendicular Lines slopes are the opposite reciprical -1 m Ex. 1 Perpendicular or Parallel? </li> <li> Slide 12 </li> <li> Parallel Lines slopes are the same (m) Perpendicular Lines slopes are the opposite reciprical -1 m Ex. 1 Perpendicular or Parallel? a) y = x + 2 y = x 9 </li> <li> Slide 13 </li> <li> Parallel Lines slopes are the same (m) Perpendicular Lines slopes are the opposite reciprical -1 m Ex. 1 Perpendicular or Parallel? a) y = x + 2 || y = x 9 </li> <li> Slide 14 </li> <li> Parallel Lines slopes are the same (m) Perpendicular Lines slopes are the opposite reciprical -1 m Ex. 1 Perpendicular or Parallel? a) y = x + 2 || b) y = 3x 5 y = x 9 y = -x + 7 </li> <li> Slide 15 </li> <li> Parallel Lines slopes are the same (m) Perpendicular Lines slopes are the opposite reciprical -1 m Ex. 1 Perpendicular or Parallel? a) y = x + 2 || b) y = 3x 5 _|_ y = x 9 y = -x + 7 </li> <li> Slide 16 </li> <li> Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. </li> <li> Slide 17 </li> <li> 1)Find the slope needed. </li> <li> Slide 18 </li> <li> 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. </li> <li> Slide 19 </li> <li> 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 </li> <li> Slide 20 </li> <li> 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 </li> <li> Slide 21 </li> <li> 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 </li> <li> Slide 22 </li> <li> 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 </li> <li> Slide 23 </li> <li> 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 = -x + 3 </li> <li> Slide 24 </li> <li> 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 = -x + 3 m = - </li> <li> Slide 25 </li> <li> 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 = -x + 3 m = -, m = 4 </li> <li> Slide 26 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; slope to write equation. </li> <li> Slide 27 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; slope to write equation. </li> <li> Slide 28 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; slope to write equation. </li> <li> Slide 29 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; slope to write equation. y y 1 = m(x x 1 ) </li> <li> Slide 30 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; slope to write equation. y y 1 = m(x x 1 ) y </li> <li> Slide 31 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; slope to write equation. y y 1 = m(x x 1 ) y </li> <li> Slide 32 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; slope to write equation. y y 1 = m(x x 1 ) y </li> <li> Slide 33 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; slope to write equation. y y 1 = m(x x 1 ) y (-2) = </li> <li> Slide 34 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; slope to write equation. y y 1 = m(x x 1 ) y (-2) = </li> <li> Slide 35 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; slope to write equation. y y 1 = m(x x 1 ) y (-2) = </li> <li> Slide 36 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; slope to write equation. y y 1 = m(x x 1 ) y (-2) = 4(x - </li> <li> Slide 37 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; slope to write equation. y y 1 = m(x x 1 ) y (-2) = 4(x - </li> <li> Slide 38 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; slope to write equation. y y 1 = m(x x 1 ) y (-2) = 4(x - </li> <li> Slide 39 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; slope to write equation. y y 1 = m(x x 1 ) y (-2) = 4(x (-3)) </li> <li> Slide 40 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; slope to write equation. y y 1 = m(x x 1 ) y (-2) = 4(x (-3)) y + 2 = 4(x + 3) </li> <li> Slide 41 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; 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 </li> <li> Slide 42 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; 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 </li> <li> Slide 43 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; 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 </li> <li> Slide 44 </li> <li> 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 = -x + 3 m = -, m = 4 2) Use coordinate point &amp; 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 </li> <li> Slide 45 </li> <li> Ex. 3 Write the slope-intercept form of the equation through (9, 0) parallel to the graph of y = - x + 2. </li> <li> Slide 46 </li> <li> 1) Find the slope needed. y = -x + 2 m = -, m || = - </li> <li> Slide 47 </li> <li> Ex. 3 Write the slope-intercept form of the equation through (9, 0) parallel to the graph of y = -x + 2. 1) Find the slope needed. y = -x + 2 m = -, m || = - 2) Use coordinate point &amp; slope to write equation. y y 1 = m(x x 1 ) y (0) = - (x (9)) y = - (x 9) y = - x + 3 </li> </ul>

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