# Find the slope of the line 1 and line 2. Is each pair of lines parallel, parpendicular, or neither? Line 1: passes through (0,6)and (3,-24) Line 2: passes through (-1,19) and (8,-71)

${m}_{12} = - 10$

${m}_{34} = - 10$

Hence, the lines are parallel

#### Explanation:

$\left({x}_{1} , {y}_{1}\right) \equiv \left(0 , 6\right)$

$\left({x}_{2} , {y}_{2}\right) \equiv \left(3 , - 24\right)$

Slope
${m}_{12} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{- 24 - 6}{3 - 0} = - \frac{30}{3} = - 10$

$\left({x}_{3} , {y}_{3}\right) \equiv \left(- 1 , 19\right)$

$\left({x}_{4} , {y}_{4}\right) \equiv \left(8 , - 71\right)$

Slope
${m}_{34} = \frac{{y}_{4} - {y}_{3}}{{x}_{4} - {x}_{3}} = \frac{- 71 - 19}{8 - \left(- 1\right)} = - \frac{90}{9} = - 10$

${m}_{12} = - 10$

${m}_{34} = - 10$

Hence, the lines are parallel