Question

two lines are considered to be parallel if they have the same slope. select the two lines below that would be parallel to each other by finding the slopes of the points shown. line a: (-1, -2) and (1, 0) line b: (4, 2) and (2, -2) line c: (0, 2) and (-1, 1)

Explanation:

Step1: Recall slope formula

The slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Calculate slope of Line A

For Line A with points \((-1, -2)\) (\(x_1=-1,y_1 = - 2\)) and \((1, 0)\) (\(x_2 = 1,y_2=0\)):
\(m_A=\frac{0-(-2)}{1-(-1)}=\frac{0 + 2}{1 + 1}=\frac{2}{2}=1\)

Step3: Calculate slope of Line B

For Line B with points \((4, 2)\) (\(x_1 = 4,y_1=2\)) and \((2, -2)\) (\(x_2=2,y_2=-2\)):
\(m_B=\frac{-2 - 2}{2 - 4}=\frac{-4}{-2}=2\)

Step4: Calculate slope of Line C

For Line C with points \((0, 2)\) (\(x_1 = 0,y_1=2\)) and \((-1, 1)\) (\(x_2=-1,y_2=1\)):
\(m_C=\frac{1 - 2}{-1 - 0}=\frac{-1}{-1}=1\)
Since \(m_A=m_C = 1\), Line A and Line C are parallel.

Answer:

Line A: \((-1, -2)\) and \((1, 0)\), Line C: \((0, 2)\) and \((-1, 1)\)