How do you find the equation of the line through the points (4,5) that is perpendicular to the line 3x-4y=7?

1 Answer
Noah G
Jun 11, 2016

The important fact about perpendicular lines is that the slope of a line perpendicular to one line is the negative reciprocal of slope of the initial line.

Explanation:

Let's first convert to slope intercept form, #y = mx + b#. This can be done by isolating #y#.

#3x - 4y = 7#

#-4y + 7 - 3x#

#y = -7/4 + 3/4x#

#:.# The slope of this line is #3/4#. Therefore, the slope of the line perpendicular will be #-4/3#.

Now, by point slope form we have:

#y - y_1 = m(x - x_1)#

#y - 5 = -4/3(x - 4)#

#y - 5 = -4/3x + 16/3#

#y = -4/3x + 31/3#

Hopefully this helps!

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