Question

assignment: 4.3a part lines
determine which of the lines, if any, are parallel.

1. 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 $(-1,1)$.

Explanation:

Step1: Calculate slope of Line a

Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
For Line a with points $(-1,-2)$ and $(1,0)$:
$m_a = \frac{0 - (-2)}{1 - (-1)} = \frac{2}{2} = 1$

Step2: Calculate slope of Line b

For Line b with points $(4,2)$ and $(2,-2)$:
$m_b = \frac{-2 - 2}{2 - 4} = \frac{-4}{-2} = 2$

Step3: Calculate slope of Line c

For Line c with points $(0,2)$ and $(-1,1)$:
$m_c = \frac{1 - 2}{-1 - 0} = \frac{-1}{-1} = 1$

Step4: Compare slopes

Parallel lines have equal slopes. $m_a = m_c = 1$, while $m_b = 2$ is different.

Answer:

Line a and Line c are parallel.