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Math Help - 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 y = mx + c

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

    I know how to calculate m:

     <br />
m = (y2 - y1)/(x2 - x1) = 3/4<br />
    but not y, x and c ....

    so this is what I'v got

    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 y = mx + c

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

    I know how to calculate m:

     <br />
m = (y2 - y1)/(x2 - x1) = 3/4<br />
    but not y, x and c ....

    so this is what I'v got

    y = (3/4)x + c


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

    y - y_1 = m(x - x_1)

    and solve for 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 y \:= \:mx + c

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

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

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

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

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

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

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

    **

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

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

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

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


    This is good way to check our answer.

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