anonymous
  • anonymous
passing through (4,-2) and perpendicular to x=5/4y-2. Write in slope intercept form.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
@zepdrix
zepdrix
  • zepdrix
is the negative 2 also in the denominator? It's a little hard to read correctly without brackets.\[\large x=\frac{5}{4y-2}\]
zepdrix
  • zepdrix
\[\large x=\frac{5}{4}y-2\]Oh like this? :) That would make more sense lol

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anonymous
  • anonymous
no it isn't. it's like the second one you just put up.
zepdrix
  • zepdrix
Let's first get our line into slope-intercept form, so we can accurately identify the slope. We want it in this form,\[\large y=mx+b\] \[\large x=\frac{5}{4}y-2\]Start by adding 2 to each side,\[\large x+2=\frac{5}{4}y\]Multiply each side by 4/5,\[\large \frac{4}{5}(x+2)=\left(\frac{5}{4}y\right)\frac{4}{5}\]The fractions will cancel out on the right, giving us,\[\large y=\frac{4}{5}x+\frac{8}{5}\] So we've got our line in slope-intercept form, this will make it easier to work with. Understand those steps so far?
anonymous
  • anonymous
oh i had put a -4/5
anonymous
  • anonymous
but yes other than that i get it so far
zepdrix
  • zepdrix
So it looks like our slope \(\large m\) is \(\large \dfrac{4}{5}\). Do you know what it means for a line to be `perpendicular`? It relates to the slope. :) Since the line we're trying to form is perpendicular to this line, it will have a slope that is a `negative reciprocal` of this slope. Do you understand what that means? c:
anonymous
  • anonymous
-4/5 correct? that would be the reciprocal
zepdrix
  • zepdrix
Hmm I believe it's going to be, -5/4. Yes the negative looks good. But then we take the reciprocal (the flip) of our fraction.
anonymous
  • anonymous
oh okay
zepdrix
  • zepdrix
So we're trying to form an equation for a line perpendicular to the given line. Let's call this new line something likeeeee \(\large y_p\). So we're trying to get an equation for this line, \(\large y_p=mx+b\). We've determined that the slope is, \(\large m=-\dfrac{5}{4}\). Now we need to find the \(\large b\) value, the `y-intercept`. To do so, we'll plug in the coordinate pair they gave us, that this line passes through.
zepdrix
  • zepdrix
So plug \(\large (4,-2)\) into our equation \(\large y_p=-\dfrac{5}{4}x+b\).
anonymous
  • anonymous
okay
anonymous
  • anonymous
i think im messing up so where
anonymous
  • anonymous
for som reason im getting y=-4/5x+6/5
anonymous
  • anonymous
i mean -5/4x+6/5
zepdrix
  • zepdrix
So plugging in our point gives us,\[\large -2=-\frac{5}{4}(4)+b\]The 4's will cancel out,\[\large -2=-\frac{5}{\cancel4}(\cancel4)+b\]Giving us,\[\large -2=-5+b\]Adding 5 to each side,\[\large b=3\] Did you do something different?
anonymous
  • anonymous
yeah i did
anonymous
  • anonymous
i was doing it wrong
anonymous
  • anonymous
so y=4/5x+8/5 is correct?
zepdrix
  • zepdrix
This was the equation of the line we started with, \[\large y=\frac{4}{5}x+\frac{8}{5}\] They gave us a bunch of information to find a different line. And that was this line,\[\large y_p=mx+b\] We determined that the slope is \(\large m=-\dfrac{5}{4}\). And that the y-intercept is \(\large b=3\).
zepdrix
  • zepdrix
The p doesn't mean anything, you don't need to put that if you don't want. It was just so we could tell it apart from our original y, which referred to a different line.
anonymous
  • anonymous
so the answer is y=-5/4x+3
zepdrix
  • zepdrix
ya :)

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