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Thread: 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 $\displaystyle m$:

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

    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 $\displaystyle m$:

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

    Hello,

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

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

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

    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 $\displaystyle m$:

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

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

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

    $\displaystyle
    y=\frac{2}{7}x
    $

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

    $\displaystyle
    y=3
    $

    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 $\displaystyle P(x_1,y_1)$ and the slope $\displaystyle m$
    . . the line through point $\displaystyle P$ with slope $\displaystyle m$ is:
    . . . . . $\displaystyle y - y_1\:=\:m(x-x_1)$


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

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


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

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

    ** [rant]

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


    Did you know that some textbooks teach you four formulas?

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

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

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

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


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

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

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

    [/rant]
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