What is the equation of the line that passes through #(3,7)# and is perpendicular to #2x+5y-7=0#?

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Answer 1 · 2018-07-27T10:16:33

#5x-2y-1=0#

The slope #m# of the line which is perpendicular to the given line: #2x+5y-7=0# is given as

#m=-1/{\text{slope of line:}\ 2x+5y-7}#

#=-1/{-2/5}#

#=5/2#

Now, the equation of the line with slope #m=5/2# & passing through the point #(x_1, y_1)\equiv(3, 7)# is given by following formula:

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

#y-7=5/2(x-3)#

#2y-14=5x-15#

#5x-2y-1=0#