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Point-Slope Form and Writing Linear Equations LESSON 5-4 Lesson Quiz 2 3 1.  Graph the equation  y  + 1 = –( x  – 3). 2.  ...
5-5 Parallel and Perpendicular Lines California Content Standards 7.0   Derive linear equations by using the point-slope f...
What You’ll Learn…And Why <ul><li>To determine whether lines are parallel </li></ul><ul><li>To determine whether lines are...
Slopes of Parallel Lines <ul><li>Nonvertical lines are parallel if </li></ul><ul><li>Any two vertical lines are parallel. ...
Slopes of Perpendicular Lines <ul><li>Two lines are perpendicular if the product of their slopes is  </li></ul><ul><li>A v...
Vocabulary <ul><li>Parallel lines are  lines in the same plane that never intersect.  Equations have the same slope, diffe...
Write an equation for the line that contains (–2, 3) and is parallel to  y  =  x  – 4. 5 2 5 2 Step 1     Identify the slo...
Write an equation for the line that contains  (–2, 3) and is parallel to  y  =  x  – 4. Step 2   Write the equation of the...
The line in the graph represents the street in front of a new house. The point is the front door. The sidewalk from the fr...
CA Standards Check <ul><li>1)  Write an equation for the line that contains (2,-6) and is parallel to y=3x +9. </li></ul>P...
CA Standards Check <ul><li>2a)  Write an equation for the line that contains (1,8)  and is perpendicular to y=3/4x + 1. </...
CA Standards Check <ul><li>2b)  Using the diagram in Ex 2, rite an equation in slope-intercept form for a new sidewalk per...
Closure: Compare the equations of non-vertical parallel line, and perpendicular lines. Parallel lines have the same slope,...
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5.5 parallel perp lines

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Transcript of "5.5 parallel perp lines"

  1. 1. Point-Slope Form and Writing Linear Equations LESSON 5-4 Lesson Quiz 2 3 1. Graph the equation y + 1 = –( x – 3). 2. Write an equation of the line with slope – that passes through the point (0, 4). 3. Write an equation for the line that passes through (3, –5) and (–2, 1) in point-slope form and slope-intercept form. 4. Is the relationship shown by the data linear? If so, model that data with an equation. – 10 – 7 0 5 20 – 3 – 1 5 x y 2 5 yes; y + 3 = ( x – 0) 6 5 6 5 7 5 y + 5 = – ( x – 3); y = – x – y – 4 = – ( x – 0), or y = – x + 4 2 3 2 3
  2. 2. 5-5 Parallel and Perpendicular Lines California Content Standards 7.0 Derive linear equations by using the point-slope formula. Master 8.0 Understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Find the equation of a line perpendicular to a given line that passes through a given point. Develop Master Page 86
  3. 3. What You’ll Learn…And Why <ul><li>To determine whether lines are parallel </li></ul><ul><li>To determine whether lines are perpendicular </li></ul><ul><li>To use parallel and perpendicular lines to plan a bike path. </li></ul>
  4. 4. Slopes of Parallel Lines <ul><li>Nonvertical lines are parallel if </li></ul><ul><li>Any two vertical lines are parallel. </li></ul><ul><li>Example the equations </li></ul><ul><li>Have the same slope, , and different y-intercept. The graphs of the two equations are parallel. </li></ul>They have the same slope and different y-intercepts
  5. 5. Slopes of Perpendicular Lines <ul><li>Two lines are perpendicular if the product of their slopes is </li></ul><ul><li>A vertical and horizontal line are also perpendicular. </li></ul><ul><li>Example The slope of </li></ul><ul><li>The slope of y = 4x + 2 is 4. Since </li></ul><ul><li>The graphs of the two equations are perpendicular. </li></ul>- 1
  6. 6. Vocabulary <ul><li>Parallel lines are lines in the same plane that never intersect. Equations have the same slope, different y-intercepts. </li></ul><ul><li>Perpendicular lines are lines that intersect to form right angles. Equations have the opposite and reciprocal slopes. </li></ul><ul><li>The product of a number and its negative reciprocal is -1. </li></ul>
  7. 7. Write an equation for the line that contains (–2, 3) and is parallel to y = x – 4. 5 2 5 2 Step 1   Identify the slope of the given line. y = x – 4 slope
  8. 8. Write an equation for the line that contains (–2, 3) and is parallel to y = x – 4. Step 2   Write the equation of the line through (–2, 3) using slope-intercept form. (Continued) y – y 1 = m ( x – x 1 ) Use point-slope form. y – 3 = x + 5 Simplify. 5 2 y = x + 8 Add 3 to each side and simplify. 5 2 y – 3 = ( x + 2 ) Substitute (2,3) for ( x 1 , y 1 ) and for m . 5 2 5 2 5 2
  9. 9. The line in the graph represents the street in front of a new house. The point is the front door. The sidewalk from the front door will be perpendicular to the street. Write an equation representing the sidewalk. Step 1  Find the slope m of the street. Step 2 Find the negative reciprocal of the slope. m = = = = – Points (0, 2) and (3, 0) are on the street. y 2 – y 1 x 2 – x 1 0 – 2 3 – 0 – 2 3 2 3 The equation for the sidewalk is y = x – 3. 3 2 The negative reciprocal of – is . So the slope of the sidewalk is . The y- intercept is –3. 2 3 3 2 3 2
  10. 10. CA Standards Check <ul><li>1) Write an equation for the line that contains (2,-6) and is parallel to y=3x +9. </li></ul>Parallel lines: same slope, different y-intercepts. Point Slope y – y 1 = m (x – x 1 ) - 6 2 3 y + 6 = 3(x – 2 ) y + 6 = 3 x – 6 – 6 – 6 y = 3 x – 12
  11. 11. CA Standards Check <ul><li>2a) Write an equation for the line that contains (1,8) and is perpendicular to y=3/4x + 1. </li></ul>Perpendicular lines: Opposite and reciprecal slopes. Point Slope y – y 1 = m (x – x 1 ) 8 1 24 y – 8 = (x – 1 ) y – 8 = x + y = x + 8 = 3 + 8 + .
  12. 12. CA Standards Check <ul><li>2b) Using the diagram in Ex 2, rite an equation in slope-intercept form for a new sidewalk perpendicular to the street from a front door at (-1, -2). </li></ul>Point Slope y – y 1 = m (x – x 1 ) (-1) (-2) -3 y + 1 = (x + 2 ) -1 = 3 y = x - 3 y + 1 = x - - 1 - . y = x -
  13. 13. Closure: Compare the equations of non-vertical parallel line, and perpendicular lines. Parallel lines have the same slope, but different y-intercepts. Perpendicular lines have slopes that are negative reciprocals of each other.
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