What is the equation of the line passing through #(31,32)# and #(1,2)#?

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Answer 1 · 2016-06-18T11:39:01

#y-32=1(x-31)#

#Slope=(31-1)/(32-2)=1#

#y-32=1(x-31)#

Answer 2 · 2016-06-20T18:28:24

#y = x +1#

There is a VERY useful formula for finding the equation of a straight line if we are given two points on the line.

It is quicker and easier than any other method I know and involves substituting ONCE, then some simplifying.

The formula is based on the fact that a straight line has a constant slope.

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

Call the two points #(x_1, y_1) and (x_2, y_2)#.
I will use B(1,2) as #(x_1, y_1)# and A(31,32) as #(x_2, y_2)#

Do not substitute for #x and y# - they are the #x and y# in the equation #y= mx +c#

#(y - 2)/(x-1) = (32 - 2)/(31-1) = 30/30 = 1/1 " simplify the fraction"#

#(y - 2)/(x-1) = 1/1 " now cross-multiply"#

#y - 2 = x - 1 " multiply out and change to standard form"#

#y = x - 1 + 2#

#y = x +1#