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Finding the Equation of a Line Given a Point and a Slope

If we have a point, ( x1 , y1 ) , and a slope, m, here's the formula we
use to find the equation of a line:

 

y - y1 = m ( x - x1 )

It's called the point-slope formula
(Duh!)

You are going to use this a LOT!

Luckily, it's pretty easy -- let's just do one:

Let's find the equation of the line that passes through the point
( 4 , -3 ) with a slope of -2:

y - y1 = m ( x - x1 ) ... m = -2 ... using the point ( 4 , -3 ), x1 is 4 and y1 is -3

Just stick the stuff in and clean it up!

y - ( -3 ) = -2 ( x - 4 ), which gives y + 3 = -2x + 8 ...be careful here! ...subtract 3 from both sides, which gives y = -2x + 5 ...done

TRY IT:

Find the equation of the line that passes through the point ( -2 , 6 ) with a slope of 3.