Results 1 to 2 of 2

Math Help - equation of a line

  1. #1
    Senior Member euclid2's Avatar
    Joined
    May 2008
    From
    Ottawa, Canada
    Posts
    400
    Awards
    1

    equation of a line

    Determine the equation of a line with an x-intercept of 4 and passing through the point(5,2)

    Am I doing it correctly?
    y = m(x - p) + q
    y=4(x-5)+2
    y=4x-20+2
    y=4x-18

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Sep 2007
    Posts
    528
    Awards
    1
    Quote Originally Posted by euclid2 View Post
    Determine the equation of a line with an x-intercept of 4 and passing through the point(5,2)

    Am I doing it correctly?
    y = m(x - p) + q
    y=4(x-5)+2
    y=4x-20+2
    y=4x-18

    Thanks
    Explanation:
    You know 2 points which are (4, 0) [as you are told it passes x-axis through x=4 which occurs when y=0] and (5,2).

    An equation of a straight line is in the form: y=mx+c where x and y are your variables, m is your gradient and c is your y-intercept.

    Gradient is calculated by m = \frac{y_1-y_2}{x_1 - x_2} where (x_1, y_1) and (x_2, y_2) are two co-ordinates.

    Use this gradient value and any co-ordinates to find the general form of the equation using y-y_1 = m (x - x_1) where (x_1, y_1) are any co-ordinates of the line.


    The method and working out:
    The two co-ordinates are (4, 0) and (5,2).

    m = \frac{y_1-y_2}{x_1 - x_2} = \frac{2-0}{5-4} = \frac21 = 2

    y-y_1 = m (x - x_1) \implies y-0 = 2(x-4) \implies y = 2x-8

    Check this with the other co-ordinates, (5,2).

    y = 2x-8 \implies 5 = 2(2) - 8

    Therefore the equation of the line is y=2x-8.
    Last edited by Simplicity; July 10th 2008 at 10:29 AM. Reason: Grammer, Spelling ^_^
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: March 18th 2011, 10:36 AM
  2. Replies: 9
    Last Post: July 31st 2009, 05:39 AM
  3. Replies: 11
    Last Post: June 2nd 2009, 06:08 PM
  4. Replies: 5
    Last Post: October 13th 2008, 10:16 AM
  5. equation of a line perpendicular to the line defined
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: June 6th 2007, 09:02 AM

Search Tags


/mathhelpforum @mathhelpforum