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 $y= mx +c$

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

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

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

$y = x - 1 + 2$

$y = x +1$

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