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Lilmike234

  • one year ago

What is the equation, in standard form, of the line passing through the points (2,3) and (4,2) ?

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  1. mathstudent55
    • one year ago
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    First, find the slope of the line. You can use the two given points for that.

  2. mathstudent55
    • one year ago
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    The slope of the line that passes through points \((x_1, y_1)\) and \((x_2, y_2) \) is \(slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} \)

  3. mathstudent55
    • one year ago
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    To find the slope, subtract the y-coordinates, and divide by the difference of the x-coordinates. Make sure you subtract the y-coordinates and the x-coordinates in the same order. Can you try this and tel me what you get?

  4. lilmike234
    • one year ago
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    -1/2 ?

  5. mathstudent55
    • one year ago
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    Correct. |dw:1437619975077:dw|

  6. mathstudent55
    • one year ago
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    Notice what I did above. I did it both ways. Using one point first one time and the other point first the other time to do the subtractions. It does not matter which point you choose as the first point. The important thing is to not mix the order when you subtract. As you can see both ways give the same answer, and you got it right.

  7. mathstudent55
    • one year ago
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    Now that we have the slope, we do the next step.

  8. mathstudent55
    • one year ago
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    The equation of a line given two points is: \(y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1} (x - x_1)\) or simply \(y - y_1 = m (x - x_1)\) when you let m = the slope. y and x above are the y and x of the equation. \(x_1\) and \(y_1\) are the x- and y-coordinates, respectively, of a point on the line.

  9. mathstudent55
    • one year ago
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    We already have the slope, so we can use the form \(y - y_1 = m(x - x_1)\) Since we know the \(slope = m = -\dfrac{1}{2} \), we replace m with the slope \(y - y_1 = -\dfrac{1}{2} (x - x_1) \)

  10. mathstudent55
    • one year ago
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    All that is left to do is to replace \(x_1\) and \(y_1\) with the coordinates of one of the points. You can use whichever point you want of the two given points.

  11. mathstudent55
    • one year ago
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    Let's use point (2, 3). We replace \(x_1\) with 2 and \(y_1\) with 3. \(y - 3 = -\dfrac{1}{2}(x - 2)\)

  12. mathstudent55
    • one year ago
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    You already have the equation of the line. Now you can put the equation in standard form or slope-intercept form if you'd like to.

  13. lilmike234
    • one year ago
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    y=5/2x+8

  14. lilmike234
    • one year ago
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    ?

  15. mathstudent55
    • one year ago
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    \(y - 3 = -\dfrac{1}{2}(x - 2)\) \(2y - 6 = -(x - 2) \) \(2y - 6 = -x + 2\) \(2y = -x + 8\) \(y = -\dfrac{1}{2} x + 4\)

  16. lilmike234
    • one year ago
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    The answer choices are 1. y=5/2x+8 2. 5x+2y=16 3. 2x-3y=9 4. 5x-2y=16

  17. mathstudent55
    • one year ago
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    Are you sure those are the choices of the same problem?

  18. lilmike234
    • one year ago
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    Yes

  19. mathstudent55
    • one year ago
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    Can't be.

  20. mathstudent55
    • one year ago
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    We have a slope of -1/2 None of those choices have a slope of -1/2

  21. lilmike234
    • one year ago
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    Well those were the answer choices

  22. mathstudent55
    • one year ago
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    Let's look at your choices and put every equation in the slope intercept form, y = mx + b. 1. y=5/2x+8 slope = 5/8 2. 5x+2y=16 2y = -5x + 16 y = -5/2 x + 8 slope -5/8 3. 2x-3y=9 -3y = -2x + 9 y = 2/3 x - 3 slope 2/3 4. 5x-2y=16 -2y = -5x + 16 y = 5/2x - 8 slope 5/2 As you can see, none of your choices have slope -1/2 None of them are answer to this question. Are you sure these are the given answers to this question and are you sure you copied the points correctly when you posted the question?

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