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anonymous

  • one year ago

Can someone check my answers please? I'm really struggling with this. Write an equation in point-slope form for the line through the given point with the given slope.

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  1. anonymous
    • one year ago
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    (8,3); m=6 (1 point) y+3=6(x-8) y-3=6(x-8) y-3=6(x+8) <-- My answer. y+3=6x+8

  2. SolomonZelman
    • one year ago
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    \(\LARGE y-\color{green}{y_1}=\color{blue}{\rm m}(x-\color{red}{x_1})\) where your point is \(\LARGE \left(\color{red}{x_1},\color{green}{y_1}\right)\) and your slope is \(\LARGE \rm \color{blue}{m}\)

  3. SolomonZelman
    • one year ago
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    in this case: \(x_1=8\) and \(y_2=3\) The slope is \(\rm m\)

  4. SolomonZelman
    • one year ago
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    and in this case, the slope is 6 (i.e. m=6)

  5. anonymous
    • one year ago
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    So, if I understand what you're saying, the answer should be B instead of C?

  6. anonymous
    • one year ago
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    if a line has a slope \(m\) and passes through a point \(x_0,y_0\) then the slope between any other point on the line \((x,y)\) and the given point \((x_0,y_0)\) must be \(m\), i.e. $$\text{slope between }(x,y)\text{ and }(x_0,y_0)=m\\\frac{y-y_0}{x-x_0}=m\\y-y_0=m(x-x_0)$$

  7. SolomonZelman
    • one year ago
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    Yes B is correct! VEry good!

  8. anonymous
    • one year ago
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    so in this case our given point is \((8,3)\) and our slope is \(6\). for any other point \((x,y)\) on our line we require that the slope between \((x,y)\) and \((8,3)\) is \(6\), so:$$\frac{y-3}{x-8}=6\\\text{so multiplying both sides by }x-8\text{ gives us: }y-3=6(x-8)$$... and this is the point-slope form

  9. anonymous
    • one year ago
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    Thank you, would you mind checking a few more? I have two days to finish and I'm terrified of getting a bad grade.

  10. SolomonZelman
    • one year ago
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    Yes, I think I can check more problems... and of course, N☼ PR☼BLEM

  11. anonymous
    • one year ago
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    now this is an unrelated, tangential note to help connect this with slope-intercept form: suppose the given point is a \(y\)-intercept, i.e. a point whose \(x\)-coordinate is zero; we can write this \((0,b)\). if we're given this \(y\)-interept and a slope \(m\), we'll find the following equation by point-slope form:$$y-b=m(x-0)$$simplifying since \(x-0=x\) we have:$$y-b=mx\\y=mx+b$$which is the normal slope-intercept form that you're familiar with

  12. anonymous
    • one year ago
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    2. Graph the equation. y+5=-2(x-4)

  13. anonymous
    • one year ago
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    I'll attach the graphs.

  14. anonymous
    • one year ago
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    unrelated note continued: in fact, given a point-slope form equation \(y-y_0=m(x-x_0)\) there is a natural way to rewrite in slope-intercept form -- simply distribute everything out and get \(y\) alone on one side: $$y-y_0=m(x-x_0)\\y-y_0=mx-mx_0\\y=\color{blue}mx+\underbrace{\color{red}{y_0-mx_0}}_{b}\\y=mx+b$$

  15. SolomonZelman
    • one year ago
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    if you got the graph why are you asked to graph it? :O

  16. SolomonZelman
    • one year ago
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    It will be easier if we go ahead and simplify this equation written in a point slope form, INTO, a y-intercept form (i.e. y=mx+b).

  17. SolomonZelman
    • one year ago
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    y+5=2(x-4) 1. expand the left side) 2. subtract 5 from both sides

  18. anonymous
    • one year ago
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  19. SolomonZelman
    • one year ago
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    oh, -2.... I missed that. apologize.

  20. SolomonZelman
    • one year ago
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    ok, you can exclude option c, because it is going up and the line with a negative slope is always going down.

  21. SolomonZelman
    • one year ago
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    y+5=-2(x-4) you can re-write it into a s y-intercept form, but you don't really have to. you know the line should go down by 2 units every time it goes 1 unit to the right (that is what a slope of -2 means). What you don't know is where do you start.... plug in x=0, to find the y-interecept.

  22. SolomonZelman
    • one year ago
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    (I mean I can tell a negative slope that is -2, and a negative slope that is not as steep as -2 right away, tho' so you can just look at the graph to see the option (the only one option) that goes 2 units down every time it goes 1 unit to the right.)

  23. anonymous
    • one year ago
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    Possibly B?

  24. SolomonZelman
    • one year ago
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    B is more like going 2 units to the right as it goes 1 down, but a slope of -2 means that we go down by 2 each time we go 1 to the right

  25. anonymous
    • one year ago
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    Then it has to be A, because I don't think D is anywhere near what we're looking at.

  26. SolomonZelman
    • one year ago
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    yes

  27. SolomonZelman
    • one year ago
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    A is Correct

  28. anonymous
    • one year ago
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    Do you have time to help with a few more?

  29. SolomonZelman
    • one year ago
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    (I am just showing an SAT kind of a technique where you can quickly identify the answer and exclude other options just using a quick look/analysis)

  30. SolomonZelman
    • one year ago
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    yes, I think so...

  31. anonymous
    • one year ago
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    Which point is located on the line represented by the equation y+4=-5(x-3)? (-4,-5) (-5,-4) (3,-4) <-- My answer. (-3,4)

  32. SolomonZelman
    • one year ago
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    Recall the point slope formula rule. I will rewrite your equation for you real quick. y-(-4)=-5(x-3) now compare that to y-y1=m(x-x1)

  33. SolomonZelman
    • one year ago
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    Yes, your answer is right

  34. anonymous
    • one year ago
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  35. anonymous
    • one year ago
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    I think D would be the correct answer for that one.

  36. SolomonZelman
    • one year ago
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    Are you sure? I am asking that because the line is not going down, it si going up....

  37. SolomonZelman
    • one year ago
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    It does go by 2 units vertically, as it goes 1 unit to the right. BUT it goes 2 units (vertically) up, not (vertically) down....

  38. anonymous
    • one year ago
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    OH! Okay! So A would be correct.

  39. SolomonZelman
    • one year ago
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    Yup

  40. anonymous
    • one year ago
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    I'm really hoping that I'm right about this one, but I think it's A.

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  41. SolomonZelman
    • one year ago
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    you got "fooled" (excuse me) by the look of it.

  42. SolomonZelman
    • one year ago
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    |dw:1436469019837:dw|

  43. anonymous
    • one year ago
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    Possibly D?

  44. SolomonZelman
    • one year ago
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    see it perfectly goes 3 units down, as it goes 8 units to the right (and although it is close to the slope of 1/2)

  45. SolomonZelman
    • one year ago
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    -8/3 slope, means: Your graph goes 8 units down as it goes 3 units to the right -3/8 slope, means: Your graph goes 3 units down as it goes 8 units to the right which one is correct if you look on our graph?

  46. anonymous
    • one year ago
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    C, I believe.

  47. SolomonZelman
    • one year ago
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    it wuld be C if it was going UP by 3 while going 8 to the right. But it goes DOWN by 3 while it goes 8 to the right. So m=-3/8

  48. anonymous
    • one year ago
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    Then it must be D.

  49. SolomonZelman
    • one year ago
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    it is B

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