Problem 31 - College Algebra

Question

If two lines are parallel, describe the relationship between their slopes.

Step-by-Step Solution

Answer

If two lines are parallel, then their slopes (the ratio of the vertical change to the horizontal change) are equal. This means that if 'm1' and 'm2' are slopes of two parallel lines, then \( m1 = m2 \).

Step 1: Understanding Slope of a Line

The slope of a line is a measure of how steep the line is. It is calculated by finding the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. In mathematical term, if two points on the line are (x1, y1) and (x2, y2), the slope 'm' is given by \( m = \frac{y2 - y1}{x2 - x1} \).

Step 2: Relation Between Slopes of Two Parallel Lines

Two lines are parallel if they have the same slope, i.e., if the ratio of the vertical change to the horizontal change is the same for both lines. This happens when they are always the same distance apart from each other, never intersecting.

Step 3: Formulate General Principle

So, if two lines are parallel, their slopes are equal. If 'm1' and 'm2' are slopes of two parallel lines, then the relationship is given by \( m1 = m2 \). This is the key principle defining the relationship between slopes of parallel lines.