How do you write the equation of the line through (4, 7) and (-2, 1) in point-slope form?

1 Answer
Ratnaker Mehta
Jul 6, 2016

#y=x+3.#

Explanation:

Eqn. of a line passing thro. pts. #(x_1,y_1) and (x_2,y_2)# is #: (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)#.

This may not turn out to be in the Point-Slope Form [in the Usual Notation ] #: y=mx+c.....................(I)#, but we can convert it in that form.

Instead, let us start with assuming the reqd. eqn. in the desired form, i.e., #(I)#.

Now, #(4,7) in [y=mx+c] rArr 7=4m+c........(1)#, & #(-2,1) in [y=mx+c] rArr 1=-2m+c............(2)#

#(1)-(2) rArr 6=6m rArr m=1# & [#m#, together with #(1)#] #rArrc=3.#

finally, we have the eqn. #:y=x+3.#

Hope, you enjoyed it, as I do!

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