How do you write an equation in standard form for a line passes through (2, –3) and is perpendicular to y = 4x + 7?

1 Answer
Alex Boroda
Jun 6, 2015

Answer: the equation of the line is #y=-1/4x -5/2#

Explanation: We have two lines: #L_1# defined by the equation #y=ax+b# and #L_2# defined by the equation #y=4x+7# #=># The slope of the line #L_2# is #4#.

We know that, If #L_1# is perpendicular to #L_2#, then the slope of #L_1# is the inverse reciprocal of the slope of #L_2#. Therefore, the slope of #L_1# is #-1/4#.

So, the equation of #L_1# is #-1/4x + b#

The line #L_1# contains the point #A(2,-3)#, therefore we have the following equation: #-3=-1/4*2+b# #=># #b=-5/2#

Therefore, the equation of #l_1# is #y=-1/4x -5/2#

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