Question

decide whether the lines given are parallel, perpendicular, or neither.
the line through $(-7, -8)$ and $(6,8)$.
the line through $(4,5)$ and $(17,21)$.

are the two lines parallel, perpendicular, or neither?
parallel
neither
perpendicular

Explanation:

Step1: Calculate slope of first line

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $(-7, -8)$ and $(6,8)$:
$m_1 = \frac{8 - (-8)}{6 - (-7)} = \frac{16}{13}$

Step2: Calculate slope of second line

Using points $(4,5)$ and $(17,21)$:
$m_2 = \frac{21 - 5}{17 - 4} = \frac{16}{13}$

Step3: Compare slopes

Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals. Here $m_1 = m_2$.

Answer:

Parallel