Final answer:
The slope-intercept form of an equation helps determine if lines are perpendicular or parallel based on the slopes of the lines.
Step-by-step explanation:
The slope-intercept form of an equation is y = mx + b, where m is the slope of the line and b is the y-intercept. When determining if two lines are perpendicular, the slopes of the lines are important. If the slope of one line is the negative reciprocal of the other, then the lines are perpendicular. The slope-intercept form makes it easy to compare the slopes of two lines and determine their relationship.
For example, let's say we have the equations y = 2x + 3 and y = -1/2x + 4. The first equation has a slope of 2 and the second equation has a slope of -1/2. The slopes are negative reciprocals of each other, so the lines are perpendicular.
When determining if two lines are parallel, the slopes again play a crucial role. If the slopes of two lines are equal, then the lines are parallel. In slope-intercept form, it is easy to compare the slopes of two lines and determine if they are parallel.
For example, let's say we have the equations y = 2x + 3 and y = 2x - 1. Both equations have a slope of 2, so the lines are parallel.
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