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Thread: Line equation from two points

  1. #1
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    Line equation from two points

    Hi

    How do I get the line equation from two points ?

    The equation is $\displaystyle y = mx + c$

    the two points are (1,2) and (5,5).

    I know how to calculate m:

    $\displaystyle
    m = (y2 - y1)/(x2 - x1) = 3/4
    $
    but not y, x and c ....

    so this is what I'v got

    $\displaystyle y = (3/4)x + c$


    Thanks
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by carel_dutoit@yahoo.co.uk View Post
    Hi

    How do I get the line equation from two points ?

    The equation is $\displaystyle y = mx + c$

    the two points are (1,2) and (5,5).

    I know how to calculate m:

    $\displaystyle
    m = (y2 - y1)/(x2 - x1) = 3/4
    $
    but not y, x and c ....

    so this is what I'v got

    $\displaystyle y = (3/4)x + c$


    Thanks
    Take one of the points given and use it as
    $\displaystyle (x_1,y_1)$, you found $\displaystyle m$ already, so just plug your values into the point-slope formula

    $\displaystyle y - y_1 = m(x - x_1)$

    and solve for $\displaystyle y$ to get the equation of the line
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  3. #3
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    Hello, Carel!

    You are that close to the answer . . .


    How do I get the line equation from two points ?

    The equation is $\displaystyle y \:= \:mx + c$

    The two points are (1,2) and (5,5).

    I know how to calculate $\displaystyle m\!:\;\;m \:= \:\frac{y_2 - y_1}{x_2 - x_1}\:= \:\frac{3}{4}$ . Right!

    So this is what I've got: .$\displaystyle y \:= \:\frac{3}{4}x + c$ . . . . Good!

    Since $\displaystyle (1,2)$ is on the line, .**
    . . then $\displaystyle x = 1,\;y= 2$ must satisfy the equation.

    Plug them into your equation: .$\displaystyle 2 \:=\:\frac{3}{4}(1) + c\quad\Rightarrow\quad c \,= \,\frac{5}{4}$ . . . see?

    . . Therefore, the equation is: .$\displaystyle y \;=\;\frac{3}{4}x + \frac{5}{4}$

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

    **

    It doesn't matter which point we use; the answer will be the same.

    Since $\displaystyle (5,5)$ is on the line,
    . . then $\displaystyle x = 5,\;y= 5$ must satisfy the equation.

    Plug them into your equation: .$\displaystyle 5 \:=\:\frac{3}{4}(5) + c\quad\Rightarrow\quad c \,= \,\frac{5}{4}$ . . . yay!

    . . Therefore, the equation is: .$\displaystyle y \;=\;\frac{3}{4}x + \frac{5}{4}$


    This is good way to check our answer.

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