Question

1. which statement is true for the slopes of parallel lines?

Explanation:

Step1: Recall the definition of parallel lines

Parallel lines are lines in a plane that do not intersect; they have the same direction.

Step2: Recall the formula for the slope of a line

The slope \( m \) of a line is defined as \( m=\frac{y_2 - y_1}{x_2 - x_1} \), which represents the rate of change of \( y \) with respect to \( x \), or the "steepness" and direction of the line.

Step3: Analyze the slopes of parallel lines

For two lines to be parallel, they must have the same steepness and direction. This means that their slopes must be equal. For example, if line \( a \) has a slope \( m_1 \) and line \( b \) is parallel to line \( a \), then \( m_1=m_2 \) (where \( m_2 \) is the slope of line \( b \)). Similarly, for lines \( p \) and \( q \), their slopes are equal.

Answer:

The slopes of parallel lines are equal.