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krissywatts

  • 3 years ago

passing through (4,-2) and perpendicular to x=5/4y-2. Write in slope intercept form.

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  1. krissywatts
    • 3 years ago
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    @zepdrix

  2. zepdrix
    • 3 years ago
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    is the negative 2 also in the denominator? It's a little hard to read correctly without brackets.\[\large x=\frac{5}{4y-2}\]

  3. zepdrix
    • 3 years ago
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    \[\large x=\frac{5}{4}y-2\]Oh like this? :) That would make more sense lol

  4. krissywatts
    • 3 years ago
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    no it isn't. it's like the second one you just put up.

  5. zepdrix
    • 3 years ago
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    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?

  6. krissywatts
    • 3 years ago
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    oh i had put a -4/5

  7. krissywatts
    • 3 years ago
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    but yes other than that i get it so far

  8. zepdrix
    • 3 years ago
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    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:

  9. krissywatts
    • 3 years ago
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    -4/5 correct? that would be the reciprocal

  10. zepdrix
    • 3 years ago
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    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.

  11. krissywatts
    • 3 years ago
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    oh okay

  12. zepdrix
    • 3 years ago
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    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.

  13. zepdrix
    • 3 years ago
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    So plug \(\large (4,-2)\) into our equation \(\large y_p=-\dfrac{5}{4}x+b\).

  14. krissywatts
    • 3 years ago
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    okay

  15. krissywatts
    • 3 years ago
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    i think im messing up so where

  16. krissywatts
    • 3 years ago
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    for som reason im getting y=-4/5x+6/5

  17. krissywatts
    • 3 years ago
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    i mean -5/4x+6/5

  18. zepdrix
    • 3 years ago
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    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?

  19. krissywatts
    • 3 years ago
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    yeah i did

  20. krissywatts
    • 3 years ago
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    i was doing it wrong

  21. krissywatts
    • 3 years ago
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    so y=4/5x+8/5 is correct?

  22. zepdrix
    • 3 years ago
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    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 \(\large b=3\).

  23. zepdrix
    • 3 years ago
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    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.

  24. krissywatts
    • 3 years ago
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    so the answer is y=-5/4x+3

  25. zepdrix
    • 3 years ago
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    ya :)

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