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

Here's a messier one -- there's something to really watch out for on the clean up!

Let's find the equation of the line that passes through the point
( -5 , 2 ) with a slope of -3 / 4.

y - y1 = m ( x - x1 )

y - 2 = - ( 3 / 4) ( x - ( -5 ) )
To clean this up, we'll multiply both sides by 4:

4 ( y - 2 ) = 4 ( -3 / 4 ) ( x + 5 ) ... Be very careful here! You only multiply the 4 into the guy in front!

4y - 8 = -3 ( x + 5 )

4y - 8 = -3x - 15 ...add 8 to both sides, which gives 4y = -3x - 7

4y = -3x - 7 ...add 3x to both sides, which gives 3x + 4y = -7

(Depending on which form you want.)

YOUR TURN:

Find the equation of the line that passes through the point ( 1 , -8 ) with a slope of 2 / 5.