Results 1 to 7 of 7

Math Help - Equation of a line (two points)

  1. #1
    Junior Member
    Joined
    Oct 2007
    Posts
    53

    Equation of a line (two points)

    This is the question I am having trouble with:

    Find the equation of the line joining each pair of given points- (-1,4) and (0,7).


    This is my working:

    Find the midpoint which is (1.5,3.5) then find the gradient which is 3. then write the equation y-3.5=3(x-1.5) then expand and rearange to form the equation 3x-y-1=0.

    My answer is correct except for the -1 part. Could someone please show mw what I did wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Paulo1913 View Post
    This is the question I am having trouble with:

    Find the equation of the line joining each pair of given points- (-1,4) and (0,7).


    This is my working:

    Find the midpoint which is (1.5,3.5) then find the gradient which is 3. then write the equation y-3.5=3(x-1.5) then expand and rearange to form the equation 3x-y-1=0.

    My answer is correct except for the -1 part. Could someone please show mw what I did wrong?
    Your midpoint is quite wrong. In fact, the point you have found (how, I don't know) does not even lie on the line. If you plotted the two given points and joined them with a straight line you'd realise this immediately.

    But why bother finding and using the midpoint??? You can use any point on the line, including (0, 7) which is the y-intercept. And you know y = mx + c .......
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2007
    Posts
    53
    I'm sorry I don't quite understand what you mean
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member nikhil's Avatar
    Joined
    Jun 2008
    Posts
    292

    Check it out

    If a and b are abcissa or ordinate of 2 points then mid point is defined as (a+b)/2 by doing so ur mid points should come (-0.5,5.5) so midpoint that u have calculated is wrong for sure. But there is no need of mid point.u can use any one of the given point.using midpoint will definetly give the answer but it will just be a unnecessary effort.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Paulo1913 View Post
    I'm sorry I don't quite understand what you mean
    What don't you understand? Using the point (0, 7)? y = mx + c?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by Paulo1913 View Post
    This is the question I am having trouble with:

    Find the equation of the line joining each pair of given points- (-1,4) and (0,7).


    This is my working:

    Find the midpoint which is (1.5,3.5) then find the gradient which is 3. then write the equation y-3.5=3(x-1.5) then expand and rearange to form the equation 3x-y-1=0.

    My answer is correct except for the -1 part. Could someone please show mw what I did wrong?
    Find an equation of a line through (-1, 4) and (0,7)

    1. Use the slope-intercept form of a linear equation:

    y=mx+b where m = slope(gradient) and b = y-intercept

    m=\frac{y_2-y_1}{x_2-x_1} = \frac{7-4}{0+1} = 3

    y-intercept = 7

    Therefore, \boxed{y=3x+7}

    2. Use the point-slope form of a linear equation:

    y-y_1=m(x-x_1) where m = slope(gradient) and x_1, y_1) is any point on the line.

    Therefore, using m = 3 and (-1, 4), we have

    \boxed{y-4=3(x+1)}

    Equations in (1.) and (2.) are equivalent.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Oct 2007
    Posts
    53
    ok I get it now. I have been rather slow lately lol
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Equation of Line from 2-points in x,y,z
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 12th 2010, 12:23 PM
  2. Finding equation of a line given two points.
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 6th 2010, 06:24 PM
  3. Replies: 11
    Last Post: May 6th 2010, 12:59 PM
  4. Replies: 2
    Last Post: March 5th 2009, 09:45 AM
  5. Line equation from two points
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: July 12th 2007, 07:07 AM

Search Tags


/mathhelpforum @mathhelpforum