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Vertical and horizontal lines

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Vertical and horizontal lines

  1. 1. Vertical and Horizontal Lines<br />Finding the equations of <br />
  2. 2. How to know which is which…<br />A vertical line will be written as x = #. Since the <br />line will have slope that is undefined, the line <br />will ONLY intersect the x axis.<br />x = 3<br />x = -1<br />x = 6<br />
  3. 3. And the other….<br />A horizontal line will be written as y = #. This <br />type of line has a zero slope, so it will only <br />intersect the y axis.<br />
  4. 4. Finding the equation<br />Find the equation of horizontal line that goes <br />through the point (8, 4)<br />Since a horizontal line is ‘flat’ line, the only way <br />to draw a line with a zero slope through that <br />point is draw a line through the y axis at 4.<br />So the line is y = 4<br />
  5. 5. Finding the equation, con’t<br />Find the equation of vertical line that goes <br />through the point (-2, 7)<br />A vertical line has an undefined slope. The only way <br />to draw a vertical line through that point is draw a <br />line through the x axis at -2.<br />So the line is x = -2<br />
  6. 6. Parallel and Perpendicular Lines<br />If you have horizontal line, you know the slope is zero, which can be <br />written as 0/1.<br />A parallel line would also have a slope of 0….another horizontal line.<br />A perpendicular line would have a slope that is the negative reciprocal <br />of that…. -1/0 <br />WHAATTT!?!?!?!?!<br />That is UNDEFINED which means a line that is perpendicular to a <br />horizontal line must be vertical .<br />
  7. 7. Example 1<br />Find the equation of line parallel to y = 6 through the <br />point (4, 2).<br />Parallel means “same slope”… and this line has a <br />slope of zero.<br />That means our parallel line must also be ‘flat’.<br />Y = 2<br />
  8. 8. Example 2<br />Find the equation of line parallel to y = 3 through the <br />point (-2, 12).<br />Parallel means “same slope”… and this line has a <br />slope of zero.<br />That means our parallel line must also be ‘flat’.<br />Y = 12<br />Seeing a pattern???<br />
  9. 9. Example 3<br />Find the equation of line parallel to y = -9 through the <br />point (13, -5).<br />Parallel means “same slope”… and this line has a <br />slope of zero.<br />That means our parallel line must also be ‘flat’.<br />Y = -5<br />When the line is parallel, keep the same variable and set it equal to that coordinate value. Soooooo….<br />
  10. 10. Example 4<br />Find the equation of line parallel to x = -9 through the <br />point (13, -5).<br />Parallel means “same slope”… and this line has a <br />slope that is UNDEFINED.<br />That means our parallel line must also be vertical.<br />x = 13<br />Now for perpendicular….<br />
  11. 11. Example 5<br />Find the equation of line perpendicular to x = 3 through the <br />point (5, 7).<br />Perpendicular means the slope will be the negative reciprocal. Our <br />original line is vertical, so the perpendicular slope will be zero…making <br />the line horizontal <br />So, we have a line that is horizontal (y = ) through the given point<br />y = 7<br />hhmmmmm….<br />
  12. 12. Example 6<br />Find the equation of line perpendicular to x = 8 through the <br />point (9 -1).<br />Perpendicular means the slope will be the negative reciprocal. Our <br />original line is vertical, so the perpendicular slope will be zero…making <br />the line horizontal <br />So, we have a line that is horizontal (y = ) through the given point<br />y = -1<br />See it yet???<br />
  13. 13. The ‘rule’<br />Parallel: keep the same variable and set it equal to the value in the point.<br />Perpendicular: that the other variable and use the value of the other variable in the point.<br />

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