Problem 55
Question
If two lines are parallel, describe the relationship between their slopes.
Step-by-Step Solution
Verified Answer
The slopes of two parallel lines are always equal.
1Step 1: Understand Parallel Lines
Parallel lines are lines in a plane that never meet; they are always the same distance apart.
2Step 2: Defining the Slope of a Line
The slope of a line in a plane containing two points, (x1, y1) and (x2, y2), is generally represented as the change in the y-coordinates divided by the change in the x-coordinates. Basically, slope = (y2 - y1) / (x2 - x1) .
3Step 3: Slope of Parallel Lines
If two lines are parallel, they have the same steepness, or gradient. To put it simply, they have the same slope. If line m is parallel to line n, and the slope of line m is a, then the slope of line n is also a. Thus, the correlation between the slopes of two parallel lines is that they are equal.
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