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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 $$- 8y - x = 43$$.