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Math Help - please help on my analytic geometry

  1. #1
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    please help on my analytic geometry

    write the equation of the line which passes through the point A with the slope m:

    1.)A(0,0), m = \frac {2}{7}
    2.)A(0,3), m = 0

    thank you very much for the help...
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  2. #2
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    write the equation of the line which passes through the point A with the slope m:

    1.)A(0,0), m = \frac {2}{7}
    2.)A(0,3), m = 0
    ...

    Hello,

    the quation of a line passing through a point P(x_1, y_1) will be described by the equation:
    \frac{y-y_1}{x-x_1}=m (point-slope-formula of a line)

    to 1: \frac{y-0}{x-0}=\frac {2}{7}. Solve for y:
    y=\frac {2}{7}x

    to 2.) \frac{y-3}{x-0}=0
    y=3

    EB
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  3. #3
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    I see

    thanks alot!
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  4. #4
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    write the equation of the line which passes through the point A with the slope m:

    1.)A(0,0), m = \frac {2}{7}
    2.)A(0,3), m = 0

    thank you very much for the help...
    The equation of a line is of the form: y=mx+c, where if x=0, y=c.

    So for 1.) c=0, and we are given m so the required equation is:

    <br />
y=\frac{2}{7}x<br />

    Similarly for 2.), c=3 and m=0 so:

    <br />
y=3<br />

    RonL
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  5. #5
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    Hello, ^_^Engineer_Adam^_^!!


    There is only one formula to learn . . . Forget the others! **

    Point-Slope Formula
    Given a point P(x_1,y_1) and the slope m
    . . the line through point P with slope m is:
    . . . . . y - y_1\:=\:m(x-x_1)


    Write the equation of the line which passes through the point A with the slope m:

    1)\;A(0,0),\;m = \frac {2}{7}
    y - 0 \:=\:\frac{2}{7}(x - 0)\quad\Rightarrow\quad y \:=\:\frac{2}{7}x


    2)\;A(0,3),\;m = 0
    y - 3 \:=\:0(x - 0)\quad\Rightarrow\quad y\:=\:3

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    ** [rant]

    These two problems can be solved easily with the form: y \:=\:mx + b
    But I find the alternate forms unnecessary/confusing/annoying.


    Did you know that some textbooks teach you four formulas?

    (1)\;y - y_1\:=\:m(x-x_1) . . . in case you're given the slope and any point

    (2)\;y \:=\:mx + b . . . in case you're given the slope and the y-intercept

    (3)\;y-y_1 \:=\:\frac{y_2-y_1}{x_2-x_1}(x-x_1) . . . in case you're given two points

    (4)\;\frac{x}{a} + \frac{y}{b} \:=\:1 . . . in case you're given the two intercepts


    (2) is unnecessary because the y-intercept is simply a point (0,b)
    . . .and we can use formula (1).

    (3) is unnecessary because, given two points, we can find the slope
    . . .with the formula: m \,=\,\frac{y_2-y_1}{x_2-x_1} ... and we can use formula (1).

    (4) is unnecessary because we are given two points (a,0) and (0,b)
    . . . The slope is: m = \frac{b-0}{0-a} = -\frac{b}{a} ... and we can use formula (1).

    [/rant]
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