Question

one line passes through the points $(-7, 5)$ and $(-1, -3)$. another line passes through points $(0, 3)$ and $(3, -1)$. are the lines parallel, perpendicular, or neither? choose 1 answer: a parallel b perpendicular c neither

Explanation:

Step1: Calculate slope of first line

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $(-7, 5)$ and $(-1, -3)$, substitute into the formula:
$m_1 = \frac{-3 - 5}{-1 - (-7)} = \frac{-8}{6} = -\frac{4}{3}$

Step2: Calculate slope of second line

For points $(0, 3)$ and $(3, -1)$, use the slope formula:
$m_2 = \frac{-1 - 3}{3 - 0} = \frac{-4}{3}$

Step3: Compare slopes

Parallel lines have equal slopes, perpendicular lines have slopes that are negative reciprocals (product is -1). Here, $m_1 = m_2 = -\frac{4}{3}$, so the slopes are equal.

Answer:

A. Parallel