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Section 3-2 : Lines

For problems 1 – 5 determine the slope of the line containing the two points and sketch the graph of the line.

  1. \(\left( {2,10} \right),\,\,\,\left( {2,14} \right)\)
  2. \(\left( { - 6,0} \right),\,\,\,\left( { - 1,3} \right)\)
  3. \(\left( {2,12} \right),\,\,\,\left( {6,10} \right)\)
  4. \(\left( { - 5,7} \right),\,\,\,\left( {1, - 11} \right)\)
  5. \(\left( { - 1, - 6} \right),\,\,\,\left( {4, - 6} \right)\)

For problems 6 – 12 write down the equation of the line that passes through the two points. Give your answer in point-slope form and slope-intercept form.

  1. \(\left( {2,10} \right),\,\,\,\left( {4,14} \right)\)
  2. \(\left( { - 6,0} \right),\,\,\,\left( { - 1,3} \right)\)
  3. \(\left( {2,12} \right),\,\,\,\left( {6,10} \right)\)
  4. \(\left( { - 5,7} \right),\,\,\,\left( {1, - 11} \right)\)
  5. \(\left( { - 1, - 6} \right),\,\,\,\left( {4, - 6} \right)\)
  6. \(\left( {0,10} \right),\,\,\,\left( {4,2} \right)\)
  7. \(\left( { - 9,2} \right),\,\,\,\left( {3,24} \right)\)

For problems 13 – 17 determine the slope of the line and sketch the graph of the line.

  1. \(6x - y = 8\)
  2. \(y + 2x = - 3\)
  3. \(3x - y = 1\)
  4. \(5y + 4x = 7\)
  5. \(6y - 13x = - 4\)

For problems 18 - 20 determine if the two given lines are parallel, perpendicular or neither.

  1. The line containing the two points \(\left( {0,0} \right)\) , \(\left( {3,18} \right)\) and the line containing the two points \(\left( { - 1, - 5} \right)\) , \(\left( {1,7} \right)\).
  2. \(y - 4x = 9\) and \(4y - x = - 3\)
  3. \(\displaystyle y = \frac{2}{3}x - 4\) and the line containing the two points \(\left( { - 4,7} \right)\) , \(\left( {2, - 2} \right)\)
  4. Find the equation of the line through \(\left( {6, - 1} \right)\) and is parallel to the line \(9x + 2y = 1\).
  5. Find the equation of the line through \(\left( {6, - 1} \right)\) and is perpendicular to the line \(9x + 2y = 1\).
  6. Find the equation of the line through \(\left( { - 4, - 9} \right)\) and is parallel to the line \( - 8y - x = 43\).
  7. Find the equation of the line through \(\left( { - 4, - 9} \right)\) and is perpendicular to the line \( - 8y - x = 43\).