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

- anonymous

- katieb

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- amistre64

parallel lines have the property that when you multiply there slope together they make (-1).

- anonymous

... Pretty sure parallel lines have the same slope.

- amistre64

get your equation into slope-intercept format: y=mx+b
y= (2/9)x - (4/9)

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- anonymous

perpendicular lines have this property, i think you may be mistaken there amistre64

- amistre64

you might be right.... lol

- amistre64

read it right, thought it wrong :) sorry

- anonymous

-5y=-7+2?

- amistre64

then we can use:
y = (2/9)x + b to figure out the line parallel with (5,-7) .... i think...

- anonymous

yes, substitute into the equation to solve for b

- 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

the parallel line might be...
y = (2/9)x + (59/9) with a little luck :)

- 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

-2x + 9y = 59
or
2x - 9y = -59 ??

- anonymous

err (y-0)=2/9(x-2) is the original line (intersects at (2,0) not (2/9,0)) sorry

- 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

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

multiplying through by 9 we have
9y + 63 = 2x - 10 -> 9y = 2x - 73 or 2x - 9y = 73

- anonymous

I still prefer point slope form for this sort of thing than slope intercept.

- amistre64

...howd I get 59? and not 73?

- 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

substituting the wrong values for x and y primarily

- amistre64

got it..... lol. I must of took the stupid pills this morning instead of the B12s :)

- 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

simple error, making a big problem, an example of the Butterfly effect in action ;)

- 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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