anonymous
  • anonymous
someone help me,im so lost on this problem..write an equation of the line containing the given point and parellel to the given line.......(5,-7);2x-9y=4
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
parallel lines have the property that when you multiply there slope together they make (-1).
anonymous
  • anonymous
... Pretty sure parallel lines have the same slope.
amistre64
  • amistre64
get your equation into slope-intercept format: y=mx+b y= (2/9)x - (4/9)

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anonymous
  • anonymous
perpendicular lines have this property, i think you may be mistaken there amistre64
amistre64
  • amistre64
you might be right.... lol
amistre64
  • amistre64
read it right, thought it wrong :) sorry
anonymous
  • anonymous
-5y=-7+2?
amistre64
  • amistre64
then we can use: y = (2/9)x + b to figure out the line parallel with (5,-7) .... i think...
anonymous
  • anonymous
yes, substitute into the equation to solve for b
amistre64
  • amistre64
5 = (2/9)(-7) + b 5 = -14/9 +b 45/9 + 14/9 = b 59/9 = b .... did i mess it up yet?
amistre64
  • amistre64
the parallel line might be... y = (2/9)x + (59/9) with a little luck :)
anonymous
  • anonymous
(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)
amistre64
  • amistre64
-2x + 9y = 59 or 2x - 9y = -59 ??
anonymous
  • anonymous
err (y-0)=2/9(x-2) is the original line (intersects at (2,0) not (2/9,0)) sorry
anonymous
  • anonymous
recall that coordinates are written (x,y) in the two dimensional plane so the x coordinate is 5, the y coordinate is -7
anonymous
  • anonymous
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)
anonymous
  • anonymous
multiplying through by 9 we have 9y + 63 = 2x - 10 -> 9y = 2x - 73 or 2x - 9y = 73
anonymous
  • anonymous
I still prefer point slope form for this sort of thing than slope intercept.
amistre64
  • amistre64
...howd I get 59? and not 73?
anonymous
  • anonymous
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)
anonymous
  • anonymous
substituting the wrong values for x and y primarily
amistre64
  • amistre64
got it..... lol. I must of took the stupid pills this morning instead of the B12s :)
anonymous
  • anonymous
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.
anonymous
  • anonymous
simple error, making a big problem, an example of the Butterfly effect in action ;)
anonymous
  • anonymous
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

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