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

Answer 1

Line A and Line C are parallel

Explanation:

Slope Equation:
`m=(y_(2) - y_(1))/(x_(2) - x_(1))`

Step 1: Find the slope of the first line

Line a passes through (-1, -2) and (1, 0).

`m = ((0- (-2)))/((1 - (-1)))`

`m=(2)/(2)`

`m=1`

Step 2: Find the slope of the second line

Line b passes through (4, 2) and (2, -2).

`m = ((-2- 2))/((2 - 4))`

`m = (-4)/(-2)`

`m=2`

Step 3: Find the slope of the third line.

Line c passes through (0, 2) and (-1, 1).

`m=((1-2))/((-1 - 0))`

`m=(-1)/(-1)`

`m=1`

Answer: Line A and Line C are parallel