Question

determine if the two lines are parallel, perpendicular, or neither. explain.
line 1: (2, 4), (5, 10)
line 2: (5, -4), (0, 6)
parallel, since the slopes are equal
perpendicular, since the slopes are opposite reciprocals
neither, since the slopes are neither equal nor opposite reciprocals
perpendicular, since the slopes are equal
parallel, since the slopes are opposite reciprocals

Explanation:

Step1: Calculate slope of Line 1

Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
For Line 1: $(x_1,y_1)=(2,4)$, $(x_2,y_2)=(5,10)$
$m_1 = \frac{10 - 4}{5 - 2} = \frac{6}{3} = 2$

Step2: Calculate slope of Line 2

For Line 2: $(x_1,y_1)=(5,-4)$, $(x_2,y_2)=(0,6)$
$m_2 = \frac{6 - (-4)}{0 - 5} = \frac{10}{-5} = -2$

Step3: Compare slopes

Parallel lines have equal slopes; perpendicular lines have slopes that are opposite reciprocals (product = -1).
$m_1
eq m_2$, and $m_1 \times m_2 = 2 \times (-2) = -4
eq -1$

Answer:

neither, since the slopes are neither equal nor opposite reciprocals