How do you find a standard form equation for the line Perpendicular to the line 7x+y=49; contains the point (7,-1)?

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Answer 1 · 2016-06-12T03:27:39

# 7y - x = -14#

Given lines #L# and #L'# which are perpendicular with each other,
their respective slopes #m# and #m'# have the following relation:

#m = -1/(m')#

In the given equation, we have

#7x + y = 49#

Transform the equation to slope-intercept form to get the slope.

#=> y = -7x + 49#

#=> m = -7#

#=> m' = -1/-7#

#=> m' = 1/7#

Now, the equation of the perpendicular line will be something like

#y = 1/7x + b#

To get the y-intercept, simply substitute the coordinates of the point which we know to lie on the line

#=> -1 = 1/7(7) + b#

#=> -1 = 1 + b#

#=> b = -2#

Hence, the equation of the perpendicular line is

#y = 1/7x - 2#

or, in standard form

#7y = x - 14#

#=> 7y - x = -14#