Lineuhasaslopeof

7
4
.Linevhasaslopeof
4
7
. Are
lineuandlinevparallelorperpendicular?

1 answer

To determine whether the lines \( \text{lineu} \) and \( \text{linev} \) are parallel or perpendicular, we can compare their slopes.

The slope of \( \text{lineu} \) is given as \( \frac{7}{4} \).

The slope of \( \text{linev} \) is given as \( \frac{4}{7} \).

  1. Parallel Lines: Two lines are parallel if their slopes are equal.

    • Here, \( \frac{7}{4} \neq \frac{4}{7} \), so the lines are not parallel.
  2. Perpendicular Lines: Two lines are perpendicular if the product of their slopes is \(-1\).

    • Let's find the product of the slopes: \[ \left(\frac{7}{4}\right) \times \left(\frac{4}{7}\right) = \frac{7 \cdot 4}{4 \cdot 7} = \frac{28}{28} = 1 \] Since the product is not \(-1\), the lines are not perpendicular.

In conclusion, \( \text{lineu} \) and \( \text{linev} \) are neither parallel nor perpendicular.