my problem is:

"write an equation for the line parallel to the line -1/4y = -4 through the point (1, 8)"

can you help me with this problem please? thanks

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- Sep 25th 2009, 07:06 PM #1

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- Sep 25th 2009, 07:10 PM #2

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When you are given a point (p,q) and a slope=m, you can construct the line with slope m through point (x,y) with the following:

y-q=m(x-p)

So you got m=2 and (p,q)=(-3,-5) so just plug it in

Then you have to change it to y=mx+b, so once you plug your stuff in, multiply through on the right and add q to both sides

y=mx-mp+q

Can you make the correct substitutions?

- Sep 25th 2009, 07:13 PM #3

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- Sep 25th 2009, 07:18 PM #4

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Well if we multiply each side by $\displaystyle -4$ you get y=16

So the slope=0 cuz 16 is a constant,

So you just need the equation y=8 for the line parallel that goes through (1,8)

Let's make this general

So they give us

$\displaystyle ay=b+cx$

$\displaystyle

y=\frac{b}{a}+\frac{c}{a}x

$

So we have found that the parallel slope=$\displaystyle \frac{c}{a}$

Now we use the point slope form of the line to get (point is (q,p))

$\displaystyle y-p=\frac{c}{a}(x-q)$

Basically, always find the slope of the line given, then use the point thats given to write it as above

- Sep 25th 2009, 07:32 PM #5

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- Sep 25th 2009, 07:33 PM #6

- Sep 25th 2009, 07:36 PM #7

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- Sep 25th 2009, 10:08 PM #8

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there are various ways....the quick way is that in the equation you can see no mention of x and it is y equal to sumthing therefore it means it is a horizontal line with a gradient of 0

therefore the line parallel would also be horizontal. therefore just take the y value of the point it is passing through and make its equal to y ie $\displaystyle y=8$

the other way is changee the equation to the form y=mx+c where m is the gradient and c is the y intercept

this is to find the gradient of the parallel line.

$\displaystyle y=(0)*(x) + 16$

therefor the value of m in the parallel line eq would be 0 as well

$\displaystyle y=(0)*(x) +c$

substitute the x and y values of the point it is passing through to find the value of c

$\displaystyle 8=(0)*(1)+c$

$\displaystyle c=8$

therefore you end up with $\displaystyle y= (0)*(x) + 8$

which is the same as $\displaystyle y=8$