Standard form??

standard form is ax +by = c





so0o how do u write an equation in standard form for the line that contains each pair of points like:





1. (3,8), (6,4)





2. (-2, -1), (2,2)

Standard form??
slope = (y1-y2)/(x1-x2)


1) (8-4)/(3-6)=-4/3


2) (-1-2)/(-2-2)= 3/4





y=mx+b in slope intercept form


1) y= -4/3x + b


4= -4/3(6)+b


4=-8 + b


b=12


2) y=3/4x+b


2=3/4(2)+b


2=3/2+b


b=1/2





rearrange from s-i form to standard form


1) y=-4/3x+12


3y=-4x+36


3y+4x=36





2) y=3/4x+1/2


4y=3x+2


4y-3x=2
Reply:There are several ways of writing down the equation of a line depending on what information you are given. The slope / intercept form which has already been mentioned is only one way of looking at it. Your geometry text should give you at least one other method which is more directly revelant when you know two points through which the line passes, and it is a very useful one to commit to memory.





Call the two points which you are given (x1, y1) and (x2, y2).


Then the general form of the equation of the line passing through these two points is





(y - y1) / (x -x1) = (y2 -y1) / (x2 - x1)





So in this case , having the points (-2, -1) and ( 2, 2 ) you get





( y - (-1)) / ( x - (-2)) = ( 2 - (-1 )) / ( 2 - (-2))





which becomes : ( y + 1 ) / ( x + 2 ) = 3 / 4





(note that you have to be VERY careful with the minus signs in this, but it shouldn't be a problem if you write everything down carefully as above and don't try to take any short cuts !)





Then rearrange ( "cross multiply") to give





4( y + 1 ) = 3 ( x + 2 )





4y + 4 = 3x + 6





4y = 3x + 2





Finally, check that you haven't made any silly mistakes with the signs by putting into the equation the values for x which you have been given, and verifying that they produce the correct values for y.





Note also that it does not matter which point you call (x1, y1) and which (x2, y2) - as long as you are careful about the minus signs, you will get the same answer.