Provide an appropriate response.
-Find $ \mathrm{k} $ so that the line through $ (3, \mathrm{k}) $ and $ (1,-2) $ is parallel to $ 2 \mathrm{x}-5 \mathrm{y}=-8 $. Find $ \mathrm{k} $ so that the line is perpendicular to $ 3 x+4 y=-9 $.
A) $ -\frac{6}{5} ;-\frac{14}{3} $
B) $ \frac{14}{5} ; \frac{2}{3} $
C) $ -\frac{6}{5} ; \frac{2}{3} $
D) $ \frac{14}{5} ;-\frac{14}{3} $

Question

Quizplus · Accepted Answer

For the line to be parallel to $ 2x - 5y = -8 $, it must have the same slope, which is $\frac{2}{5}$. Using the point-slope form, solve for $ k $ to get $ k = -\frac{6}{5} $. For the line to be perpendicular to $ 3x + 4y = -9 $, its slope must be the negative reciprocal, $-\frac{4}{3}$. Solving for $ k $ gives $ k = \frac{2}{3} $.

Provide an Appropriate Response k \mathrm{k} k So That the Line Through

Provide an Appropriate Response $\mathrm{k}$ So That the Line Through