How do you write an equation in standard form given a line that passes through (-9,-3) and perpendicular to #y=-5/7*x-9#?

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Answer 1 · 2015-06-20T18:51:56

The line has equation #-7/5x+y=48/5#

we are looking for an equation of a line, that:

ad. 1

If a line #y=a_1x+b_1# is perpendicular to #y=a_2x+b_2# then #a_1*a_2=-1# so we look for a number a for which #-5/7a=-1# which makes #a=7/5#

ad. 2

Now we have to find #b# for which the line passes through #(-9,-3)#. So we substitute #x=-9# abd #y=-3# in #y=7/5x+b#

#-3=7/5*(-9)+b#
#-3=-63/5+b#
#b=63/5-15/5#
#b=48/5#

So we get the equation #y=7/5x+48/5#.

Now to transfer it to th standard form we move terms containing #x# and #y# to the left and the free term to the right, sio we get:

#-7/5x+y=48/5#