Question #c8b37

1 Answer
sente
Oct 9, 2016

#g(x) = -1/3x + 7/3#

Explanation:

Two lines #y = m_1x+b_1# and #y = m_2x+b_2# are perpendicular if and only if #m_1 = -1/m_2#

As we wish for #g(x)# to be perpendicular to a line with slope #3#, we know that #g(x)# has a slope of #-1/3#. As we are also given that #g(x)# passes through the point #(1, 2)#, we can plug these into the point-slope form of a line: #y - y_1 = m(x-x_1)# to get the graph #y = g(x)# as

#y-2 = -1/3(x-1)#

#=> y-2 = -1/3x + 1/3#

#=> y = -1/3x + 7/3#

#:. g(x) = -1/3x + 7/3#

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