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Math Help - Finding the equation of a straight line...

  1. #1
    Geo
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    Finding the equation of a straight line...

    Ok I think I've worked this out incorrectly so if someone could point me in the right direction that would be great.....

    The question is find the equation of a line that passes through (-1,5) and (2,-4)
    I know that
    y=mx+c to find M = change in y value divide by change in x value=

    2- (-1)/5-(-4) = 3/9 =1/3

    so y = 1/3x=c

    so 5=1/3(-1)+c
    5= -1/3+c
    5+-1/3 = c
    4 2/3 = c so
    y= 1/3x+ 14/3

    You see why I need help right?
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  2. #2
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    The question is find the equation of a line that passes through (-1,5) and (2,-4).

    putting the x and y values into y = mx + c we get:
    (1) 5 = -m + c
    (2) -4 = 2m + c

    (1) - (2) we get:
    5 - (-4) = -m - 2m + c - c
    9 = -3m
    m = -3

    Putting the value m=-3 into our (1)
    5 = 3 + c

    therefore c = 2

    So the equation for the line is y = -3x + 2
    I hope u can understand that.

    edit:
    What u did what "2- (-1)/5-(-4) = 3/9 =1/3"
    which is the change in x divided by the change in Y.

    Y has gone from 5 to -4 so the change in Y is -9, X has gone from -1 to 2 so the change in X is 3.
    -9/3 = -3.
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  3. #3
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    Quote Originally Posted by Geo View Post
    Ok I think I've worked this out incorrectly so if someone could point me in the right direction that would be great.....

    The question is find the equation of a line that passes through (-1,5) and (2,-4)
    You denote the equation of a line as y = mx + c . Finding the gradient of the line:

    m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - -4}{-1 - 2} = \frac{9}{-3} = -3

    Having found the gradient, we can find the equation of a line by either using the gradient-intercept form or point-gradient form:

    * Using Gradient-Intercept.

    y = mx + c : choose a given point...I'll use (2, -4)

    Thus, -4 = -3 \times {2} + c

    -4 = -6 + c

    2 = c

    Therefore, the equation of the line is y = -3x + 2

    * Using Point - Gradient method:

    y - y_1 = m(x - x_1) : again, I'll use the point (2, -4)

    y - -4 = -3(x - 2)

    y + 4 = -3x + 6

    y = -3x + 2

    Trust this helps.
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