How do you find a standard form equation for the line with (7,3); perpendicular to the line y = 4x +2?

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Answer 1 · 2016-05-29T07:02:47

#y = -1/4x + 19/4#

In general, when two lines #L# and #L'# are perpendicular, the slope of the lines are negative inverses of each other.

#m = -1/(m')#

The given equation of the line

#y = 4x + 2#

#y = mx + b#

where

#m# is the slope of the line
and #b# is the #y#-intercept

This means that the slope of the line is

#m = 4#

Hence, the slope of the line perpendicular to the given line is

#m' = -1/4#

To get the y-intercept, simply substitute the coordinate of the point which we know is on the line

#y' = m'x' + b'#

#y' = -1/4x' + b'#

#3 = -1/4(7) + b'#

#12 = -7 + 4b#

#b = 19/4#

Hence, the equation of the line is

#y = -1/4x + 19/4#