What is the equation of the line passing through the points #(3,3)# and #(-2, 17)#?

1 Answer
Alan P.
May 2, 2017

#y=-2.8x+11.4#

Explanation:

For any two points on a straight line (as given by a linear equation)
the ratio of the difference between the #y# coordinate values divided by the difference between the #x# coordinate values (called the slope) is always the same.

For the general point #(x,y)# and specific points #(3,3)# and #(-2,17)#
this means that:
the slope #=(Deltay)/(Deltax)=(y-3)/(x-3)=(y-17)/(x-(-2))=(3-17)/(3-(-2))#

Evaluating the last expression we have that
the slope #= (3-17)/(3-(-2))=(-14)/(5)=-2.8#

and therefore both
#{:((y-3)/(x-3)=-2.8,color(white)("XX")andcolor(white)("XX")(y-17)/(x-(-2))=-2.8):}#

We could use either of these to develop our equation; the first one seems easier to me (but feel free to test this with the second version to see that you get the same result).

If #(y-3)/(x-3)=-2.8#
then (assuming #x!=3#, otherwise the expression is meaningless)
after multiplying both sides by #(x-3)#
#color(white)("XX")y-3=-2.8x+8.4#
and therefore (after adding #3# to both sides)
#color(white)("XX")y=-2.8x+11.4#

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