Identify if the following lines are parallel, perpendicular, or neither(2 points)

Question

y=−34x−3
and y=34x+3

y=11x+8
and y=−111x+5

y=49x+5
and y=49x+2

y=x+4
and y=−x−7

Answer 1

To determine if the given lines are parallel, perpendicular, or neither, we need to look at the slopes of each pair of lines. Lines are parallel if they have the same slope, perpendicular if the product of their slopes is -1, and neither if neither condition is satisfied.

1. Lines: \(y = -34x - 3\) and \(y = 34x + 3\)

   • Slope of the first line: \(-34\)
   • Slope of the second line: \(34\)
   • Product of slopes: \(-34 \times 34 = -1156\) (not -1)
   • Conclusion: Neither

2. Lines: \(y = 11x + 8\) and \(y = -111x + 5\)

   • Slope of the first line: \(11\)
   • Slope of the second line: \(-111\)
   • Product of slopes: \(11 \times -111 = -1221\) (not -1)
   • Conclusion: Neither

3. Lines: \(y = 49x + 5\) and \(y = 49x + 2\)

   • Slope of the first line: \(49\)
   • Slope of the second line: \(49\)
   • Since both slopes are equal:
   • Conclusion: Parallel

4. Lines: \(y = x + 4\) and \(y = -x - 7\)

   • Slope of the first line: \(1\)
   • Slope of the second line: \(-1\)
   • Product of slopes: \(1 \times -1 = -1\)
   • Conclusion: Perpendicular

Summary:

1. Neither
2. Neither
3. Parallel
4. Perpendicular