5 8 Parallel Perpendicular Lines

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5 8 Parallel Perpendicular Lines

  1. 1. Parallel & Perpendicular Lines Section 5.8
  2. 2. Background: Slope <ul><li>If a line is in slope intercept form the slope is easy to locate. </li></ul><ul><li>Where is the slope located in slope- intercept form? </li></ul><ul><li>What is the slope of an equation of x= ? </li></ul><ul><li>What is the slope of an equation of y= ? </li></ul>
  3. 3. Background: Slope <ul><li>Standard Form </li></ul><ul><li>Let’s transform Standard Form into Slope-Intercept Form </li></ul><ul><ul><li>Ax + By = C </li></ul></ul><ul><ul><li>By = -Ax + C </li></ul></ul><ul><ul><li>y = - A/B x + C/B </li></ul></ul><ul><li>What’s the slope? </li></ul><ul><li>m = -A/B </li></ul>
  4. 4. Ex 1a: Parallel Lines <ul><li>The slope of parallel lines are exactly the same. </li></ul><ul><li>All horizontal lines are parallel and have a slope of what? </li></ul><ul><li>All vertical lines are parallel and have a slope of what? </li></ul><ul><li>Regardless of the form of the equation, you just have to find the slope and you have the slope of all the parallel lines. </li></ul>
  5. 5. Ex 1b: Parallel Lines <ul><li>In these equations, you will be given an equation and a point. </li></ul><ul><li>Find the slope of the equation. </li></ul><ul><li>(That’s all you need the equation for. You are now finished with it.) </li></ul><ul><li>Now, use the slope and the point to find the y-intercept. </li></ul><ul><li>Plug the slope and the y intercept into the equation. </li></ul>
  6. 6. Ex 2: Perpendicular Lines <ul><li>Perpendicular lines form right angles when they meet. </li></ul><ul><li>The slopes of perpendicular lines are opposite reciprocals. </li></ul><ul><li>When you multiply perpendicular slopes together, their products equal -1. </li></ul>
  7. 7. Ex 2: Perpendicular Lines <ul><li>Examples of opposite reciprocals: </li></ul><ul><li>1/3 and -3/1 </li></ul><ul><li>1 and -1 </li></ul><ul><li>-1/2 and 2/1 </li></ul><ul><li>What is the opposite reciprocal of -3/5? </li></ul><ul><li>5/3 </li></ul>
  8. 8. Review

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