Question

determine which of the lines, if any, are parallel. explain. line a passes through (-1, -2) and (1, 0). line b passes through (4, 2) and (2, -2). line c passes through (0, 2) and (-1, 1). ; the slopes are .

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Calculate slope of Line a

For Line a, points are \( (-1, -2) \) and \( (1, 0) \).
\( m_a=\frac{0 - (-2)}{1 - (-1)}=\frac{0 + 2}{1 + 1}=\frac{2}{2}=1 \)

Step3: Calculate slope of Line b

For Line b, points are \( (4, 2) \) and \( (2, -2) \).
\( m_b=\frac{-2 - 2}{2 - 4}=\frac{-4}{-2}=2 \)

Step4: Calculate slope of Line c

For Line c, points are \( (0, 2) \) and \( (-1, 1) \).
\( m_c=\frac{1 - 2}{-1 - 0}=\frac{-1}{-1}=1 \)

Step5: Compare slopes

We have \( m_a = 1 \), \( m_b = 2 \), \( m_c = 1 \). So \( m_a = m_c \), which means Line a and Line c are parallel because parallel lines have equal slopes.

Answer:

Line a and Line c are parallel; The slopes are \( m_a = 1 \), \( m_b = 2 \), \( m_c = 1 \) (so \( m_a = m_c \)).