How do you find the slope of the line parallel to and perpendicular to #y=x+3#?

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Answer 1 · 2017-08-26T12:41:28

See a solution process below:

The equation in the problem is in slope-intercept form. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

#y = x + color(blue)(3)#

or

#y = color(red)(1)x + color(blue)(3)#

Therefore the slope of the line is: #color(red)(m = 1)#

Parallel Lines

Parallel lines by definition have the same slope. Therefore, the slope of a line parallel to the line in the problem will be:

#color(red)(m = 1)#

Perpendicular Lines

Let's call the slope of a perpendicular line: #m_p#

The formula for the slope of a perpendicular line is:

#m_p = -1/m#

Substituting gives:

#m_p = -1/1 = -1#