How do you find a general form equation for the line through the pair of points (-3,8) and (4,-1)?

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Answer 1 · 2016-06-14T19:15:56

#9x+7y-29=0.#

Method I

Eqn. of a line passing thro. pts. #(a,b), (c,d)# is #(y-b)/(d-b)=(x-a)/(c-a).#

In our case, it is #(y-8)/(-1-8)=(x+3)/(4+3),# or, #(y-8)/-9=(x+3)/7,# i.e., #7y-56+9x+27=0#

Reqd. eqn. is #9x+7y-29=0.#

Method II

Slope of the reqd. line #=(8+1)/(-3-4)=-(9/7).#

it passes thro. pt.#(-3,8)#.

#:.# Its eqn. is #y-8=-(9/7)(x+3),# i.e., #7(y-8)+9(x+3)=0,# or, #9x+7y-29=0,# as before!.