Question

Consider the lines p and q.
p:y=3/5x+2
q: y =- 5/3x-1
True or False: p || q
• True
• False

Answer 1

To determine if the lines \( p \) and \( q \) are parallel, we need to examine their slopes.

The equation of line \( p \) is given by:
\[ y = \frac{3}{5}x + 2 \]
Here, the slope (m) of line \( p \) is \( \frac{3}{5} \).

The equation of line \( q \) is given by:
\[ y = -\frac{5}{3}x - 1 \]
Here, the slope of line \( q \) is \( -\frac{5}{3} \).

Two lines are parallel if they have the same slope. In this case, the slopes are \( \frac{3}{5} \) and \( -\frac{5}{3} \). Since \( \frac{3}{5} \) is not equal to \( -\frac{5}{3} \), the lines are not parallel.

Therefore, the statement "p || q" is **False**.