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parallel lines have the property that when you multiply there slope together they make (-1).
... Pretty sure parallel lines have the same slope.
get your equation into slope-intercept format: y=mx+b y= (2/9)x - (4/9)
perpendicular lines have this property, i think you may be mistaken there amistre64
you might be right.... lol
read it right, thought it wrong :) sorry
then we can use: y = (2/9)x + b to figure out the line parallel with (5,-7) .... i think...
yes, substitute into the equation to solve for b
5 = (2/9)(-7) + b 5 = -14/9 +b 45/9 + 14/9 = b 59/9 = b .... did i mess it up yet?
the parallel line might be... y = (2/9)x + (59/9) with a little luck :)
(y-0) = 2/9(x-2/9) is point slope format. This is the line with slope 2/9 which intersects the point (2/9, 0). You want the line with the same slope that intersects(5,-7) So your line would be (y+7) = 2/9(x-5)
-2x + 9y = 59 or 2x - 9y = -59 ??
err (y-0)=2/9(x-2) is the original line (intersects at (2,0) not (2/9,0)) sorry
recall that coordinates are written (x,y) in the two dimensional plane so the x coordinate is 5, the y coordinate is -7
given y=(2/9)x + b you then simply substitute into this equation using x=5; y=-7, subtract -10/9 from each side to obtain b and then write the equation in full to get the final answer: y=(2/9)x-(73/9)
multiplying through by 9 we have 9y + 63 = 2x - 10 -> 9y = 2x - 73 or 2x - 9y = 73
I still prefer point slope form for this sort of thing than slope intercept.
...howd I get 59? and not 73?
I feel that it overcomplicates the issue to what was a very simple substitution, changing from y=mc+c to (y-y0)=m(x-x0)
substituting the wrong values for x and y primarily
got it..... lol. I must of took the stupid pills this morning instead of the B12s :)
Once you get the slope (either by slope intercept or point slope) constructing the new line using point slope is far easier than using slope intercept, since you have the point and the slope, and you don't have to take the additional step of solving for the intercept.
simple error, making a big problem, an example of the Butterfly effect in action ;)
yes but in the slope intercept method generalises more naturally to higher dimensions and you start with the equation with only one unknown which intuitively feels more achievable, especially when working with the complex plane and lots of algebra it is also asthetically [certiain that is spelt incorrectly :)] more pleasing