How do you write an equation in standard form for a line passing through (–1, 2) and (3, 4)?

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Answer 1 · 2015-05-26T20:13:02

First find the slope of the line. This is (change in #y#) / (change in #x#).

For your example:

slope #= (Delta y)/(Delta x) = (4 - 2)/(3 - (-1)) = 2 / 4 = 1/2#

Slope intercept form is #y = mx + c# where #m# is the slope and #c# the intercept.

To calculate #c# we can subtract #mx# from both sides to get:

#c = y - mx#.

We know #m=1/2# and we have two example points that satisfy the equation of the line we're aiming for. Let us use #(-1, 2)#...

#c = y - mx = 2 - (1/2*-1) = 2+1/2 = 5/2#

So the equation of our line is:

#y = 1/2x + 5/2#