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Math Help - slopes

  1. #1
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    slopes

    Each pair of points is on a line. What is the slop of each line?
    A(7,5), B(2,4)

    A(5,2), B(2,-1)

    A(-3,3) B(5,3)

    Write the equation for the line passing through each pair of points

    (3,8), (2,6)

    (-2,-4), (5,-1)


    Can someone show me how to do all of these step by step?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    To calculate the slope, we use the formula (y2-y1)/(x2-x1)

    For the first set:

    A = (7,5) = (x1,y1), B = (2,4) = (x2,y2)

    => slope = (4 - 5)/(2 - 7) = -1/-5 = 1/5


    For the second set:

    A = (5,2) = (x1,y1), B = (2,-1) = (x2,y2)

    => slope = (-1 - 2)/(2 - 5) = -3/-3 = 1


    For the third set:

    A = (-3,3) = (x1,y1), B = (5,3) = (x2,y2)

    Here we notice the y value is the same in both coordinates, it means therefore that a horizontal line connects these two points, so the slope is 0. Nevertheless, let's go through the routine.

    => slope = (3 - 3)/(5 + 3) = 0/8 = 0........as expected



    Now for the equation of a line section.

    Recall that the equation of a line is in the form y = mx + b, where m is the slope and b is the y-intercept. So first we need to find the slope of the line connecting the pair of points, then we can plug it into the above formula to find b and rewrite the formula in the form above, OR we can plug the values we know into the formula y - y1 = m(x - x1), where x1 and y1 come from any one of the points given, then you just solve for y, and your equation will be in the above form--I usually use the latter approach, and that's the one I will be using. Here goes.

    For (3,8) , (2,6)

    slope = m = (6 - 8)/(2 - 3) = -2/-1 = 2

    Using (x1,y1) = (3,8)

    y - y1 = m(x - x1)

    => y - 8 = 2(x - 3)
    => y = 2x -6 + 8
    so y = 2x + 2


    For (-2,-4) , (5,-1)

    slope = m = (-1 + 4)/(5 + 2) = 3/5

    Using (x1,y1) = (5,-1)

    y - y1 = m(x - x1)

    => y + 1 = (3/5)(x - 5)
    => y = (3/5)x -3 - 1
    so y = (3/5)x - 4
    Last edited by Jhevon; February 22nd 2007 at 02:03 PM.
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