What is the equation of the line passing through #(41,89)# and #(1,2)#?

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Answer 1 · 2015-11-11T19:49:38

Use the two coordinate formula and rearrange into the form #y=mx+c#

The Two Coordinate Formula
The general form of the two coordinate formula is:

#(y-y_1)/(y_2-y_1) = (x-x_1)/(x_2-x_1)#

when you have two coordinates, #(x_1,y_1)# and #(x_2,y_2)#.

Applied to your example
The values in your example are: #x_1 = 41#, #x_2 = 1#, #y_1 = 89# and #y_2 = 2#

Substituting these into the formula we get:

#(y-89)/(2-89) = (x-41)/(1-41)#

If we evaluate the denominators we get:

#(y-89)/-87 = (x-41)/-40#

We can then multiply both sides by -87 to get rid of one fraction:

#y-89 = (-87x+3567)/-40#

Next we can multiply both sides by -40 to get rid of the other fraction:

#-40y+3560 = -87x+3567#

Next we can take away 3560 from both sides to get #-40y# on its own:

#-40y = -87x+7#

Next we can multiply by -1 to flip the signs:

#40y = 87x-7#

Finally we divide by 40 to get #y# on its own and our answer in the form #y=mx+c#:

#y = 87/40x-7/40#