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 \( (1, 0) \).
Using slope formula: \( m_a=\frac{0 - (-2)}{1 - (-1)}=\frac{0 + 2}{1 + 1}=\frac{2}{2} = 1 \).

Step3: Calculate slope of Line b

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

Step4: Calculate slope of Line c

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

Step5: Compare slopes

We have \( m_a = 1 \), \( m_b = 2 \), \( m_c = 1 \). Since \( m_a=m_c = 1 \), lines with equal slopes are parallel. So Line a and Line c have equal slopes, hence they are parallel. The slopes of Line a and Line c are equal (both 1), slope of Line b is 2 (different from the other two).

Answer:

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