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If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
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.
- \(\left( {2,10} \right),\,\,\,\left( {2,14} \right)\)
- \(\left( { - 6,0} \right),\,\,\,\left( { - 1,3} \right)\)
- \(\left( {2,12} \right),\,\,\,\left( {6,10} \right)\)
- \(\left( { - 5,7} \right),\,\,\,\left( {1, - 11} \right)\)
- \(\left( { - 1, - 6} \right),\,\,\,\left( {4, - 6} \right)\)
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.
- \(\left( {2,10} \right),\,\,\,\left( {4,14} \right)\)
- \(\left( { - 6,0} \right),\,\,\,\left( { - 1,3} \right)\)
- \(\left( {2,12} \right),\,\,\,\left( {6,10} \right)\)
- \(\left( { - 5,7} \right),\,\,\,\left( {1, - 11} \right)\)
- \(\left( { - 1, - 6} \right),\,\,\,\left( {4, - 6} \right)\)
- \(\left( {0,10} \right),\,\,\,\left( {4,2} \right)\)
- \(\left( { - 9,2} \right),\,\,\,\left( {3,24} \right)\)
For problems 13 – 17 determine the slope of the line and sketch the graph of the line.
- \(6x - y = 8\)
- \(y + 2x = - 3\)
- \(3x - y = 1\)
- \(5y + 4x = 7\)
- \(6y - 13x = - 4\)
For problems 18 - 20 determine if the two given lines are parallel, perpendicular or neither.
- The line containing the two points \(\left( {0,0} \right)\) , \(\left( {3,18} \right)\) and the line containing the two points \(\left( { - 1, - 5} \right)\) , \(\left( {1,7} \right)\).
- \(y - 4x = 9\) and \(4y - x = - 3\)
- \(\displaystyle y = \frac{2}{3}x - 4\) and the line containing the two points \(\left( { - 4,7} \right)\) , \(\left( {2, - 2} \right)\)
- Find the equation of the line through \(\left( {6, - 1} \right)\) and is parallel to the line \(9x + 2y = 1\).
- Find the equation of the line through \(\left( {6, - 1} \right)\) and is perpendicular to the line \(9x + 2y = 1\).
- Find the equation of the line through \(\left( { - 4, - 9} \right)\) and is parallel to the line \( - 8y - x = 43\).
- Find the equation of the line through \(\left( { - 4, - 9} \right)\) and is perpendicular to the line \( - 8y - x = 43\).