How do you find the equation of the line tangent to the graph of # f(x)=1/2x + 4#, (2,5)?

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Answer 1 · 2015-10-19T19:29:43

#x-2y+8=0#

Firstly, you find the slope or gradient of the tangent to the line;
you do this by comparing the given equation with #y=mx+c#:

here #m=1/2#

the formula for the equation of a line is

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

so

#(y-5)=1/2(x-2)#

#2y-10=x-2#

so

#x-2y+8=0# is the required equation