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Math Help - Equations and Given Points in Slopes

  1. #1
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    Equations and Given Points in Slopes

    Find the equation of the line that contains the given point and has the given slope:

    Point (5,1), m= 2/3

    Point (1,5), m = -4/5

    Point (0,0), m = 3/4

    Point (2,0), m = 5/6

    Point (-2,5), slope is undefined

    Point (-3,5), m = 3

    help?
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    This is not hard, all that you need is the point-slope formula, which states that

    y-y_1=m(x-x_1).

    (x_1,y_1) & m are the point and the slope respectively, so plug the values into the aforesaid formula.

    --

    When the slope is undefined, the equation which represents the line is x=-2 (for the problem #5).
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  3. #3
    Super Member angel.white's Avatar
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    I personally like y=mx+b better (prob b/c thats how I learned it)

    y = y value
    x = x value
    m = slope
    b = y-intercept

    If you want to use this format, the first one would go like this:
    Given: Point (5,1), m= 2/3

    plug in:
    y=mx+b
    1=\frac{2}{3}(5) + b

    1=\frac{10}{3}+b

    1 - \frac{10}{3} = b

    \frac{3}{3} - \frac{10}{3} = b

    \frac{3-10}{3} = b

    \frac{-7}{3} = b


    Now our slope and y-int are constants, so we just plug them into our equation:
    y=mx+b

    y=\frac{2}{3}x+\frac{-7}{3}

    this can also be written as:
    y=\frac{2}{3}x-\frac{7}{3}

    You can then use this equation to take any x value and find the y value, or any y value and find the x value, or you could take any x, y pair and with the given slope, find the y-intercept. Or any x, y pair and with the given y-intercept you could find the slope.

    We leave x and y as variables because while the slope and y-intercept are constants, there are an infinite number of x and y values which will satisfy this equation (any point on the line will have an x,y pair that will satisfy the equation). For example, you will notice that when x=8 and y=3, the equation works out as well. And we plug in the values for m and b because these are constants, they will never change no matter what part of the line you are looking at.
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