Determine if two lines with gradients 2 and −2 are parallel or perpendicular, and define perpendicular lines…

Question

Determine if two lines with gradients 2 and −2 are parallel or perpendicular, and define perpendicular lines in terms of gradients.

ScanSolve AI Tutor · Accepted Answer

Okay, thanyani, let's complete the final questions.

Answer 3.1.3
The gradients of the two graphs from 3.1.2 are $m_1 = 2$ (for $y = 2x - 2$ ) and $m_2 = -2$ (for $y = -2x + 1$ ).
- For graphs to be parallel, their gradients must be equal ( $m_1 = m_2$ ). Here, $2 \neq -2$ , so the graphs are not parallel.
- For graphs to be perpendicular, the product of their gradients must be $-1$ ( $m_1 \times m_2 = -1$ ). Here, $2 \times (-2) = -4$ , which is not equal to $-1$ , so the graphs are not perpendicular. Therefore, the two graphs are neither parallel nor perpendicular to each other.
Answer 3.1.4
This question asks for the definition of perpendicular lines in terms of their gradients.
Conclusion: If the product of the two gradients of two linear graphs is equal to $\boxed{-1}$ , therefore the linear graphs are $\boxed{\text{perpendicular}}$ to each other.

Determine if two lines with gradients 2 and -2 are parallel or perpendicular, and define perpendicular lines in terms of gradients.