Results 1 to 3 of 3

Math Help - Equation of a Line

  1. #1
    Newbie
    Joined
    Jan 2009
    From
    Toronto
    Posts
    2

    Equation of a Line

    Let me get this straight.. there are three equations:
    slope - y intercept form:
    y = mx + b
    standard form:
    ac + by + c = 0
    point- slope form:
    y - y1 = m(x + x1)

    Now: how do you convert from one form to another form? And I'm not sure I quite understand what each equation represents. For example, in standard form, what does C represent? In slope-y intercept form, what does x represent? This is so confusing.
    And the thing is, I know the information and the principles, but I can't apply it in actual math questions. Does anybody have any hints on how to learn when to use one equation rather than another, or how to solve problems with these equations?
    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by ifailatmath View Post
    Let me get this straight.. there are three equations:
    slope - y intercept form:
    y = mx + b
    standard form:
    ac + by + c = 0
    point- slope form:
    y - y1 = m(x + x1)

    Now: how do you convert from one form to another form? And I'm not sure I quite understand what each equation represents. For example, in standard form, what does C represent? In slope-y intercept form, what does x represent? This is so confusing.
    And the thing is, I know the information and the principles, but I can't apply it in actual math questions. Does anybody have any hints on how to learn when to use one equation rather than another, or how to solve problems with these equations?
    Thanks
    I'm sure for the standard form you MEANT to write  ax + by + c = 0

    Consider the following:

     ax + by + c = 0


      by  = -ax - c

      y  = \frac{-a}{b}x - \frac{c}{a}

    That is the same as slope-intercept form! The gradient of the line is given by  m = \frac{-a}{b} , and the y-intecept is the point  \big(0, \frac{-c}{a}\big) .

    The point-slope from comes from the fact that the gradient of a line, m, is defined as:

     m = \frac{y - y_1}{x - x_1}

     y - y_1 = m(x-x_1)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member mollymcf2009's Avatar
    Joined
    Jan 2009
    From
    Charleston, SC
    Posts
    490
    Awards
    1
    Originally Posted by ifailatmath
    Let me get this straight.. there are three equations:
    slope - y intercept form:
    y = mx + b
    standard form:
    ac + by + c = 0 <--This should be ax + by + c = 0
    point- slope form:
    y - y1 = m(x + x1) <-- this should actually be
    (x-x_1)

    First, think about why the name of each formula is called that.
    Slope-intercept gives you exactly what it says it does, a slope (m) and a y intercept (b)
    Point-slope also gives you what it says it does,
    y-y_1 are two y coordinates for two points somewhere on your line and x-x_1 are the two x-coordinates of those same y-coordinates of the points on your line. The slope IS already in the point-slope equation, you just haven't solved for it yet. It is a good equation to use if you are given the graph of a line and asked to find the equation of it. Look closer at the point-slope equation. If you got "m" by itself by dividing both sides by
    (x-x_1) that would be your slope right? (x-x_1) is the "run" part of your slope and (y-y_1) is the "rise" part. \frac{change in y values}{change in x values}

    1) How do you convert from one form to another form?
    I personally like slope-intercept form best. It is easy to work with because it tells you exactly where your line hits the y-intercept or "b" in that equation. You can get all of these into slope-intercept form by solving for "y"
    a) ax + by + c = 0
    by = -ax - c
    y = \frac{-ax}{b}-\frac{c}{b}
    ***a, b & c are just coefficients (the numbers in front of your variables x & y
    2) And I'm not sure I quite understand what each equation represents. For example, in standard form, what does C represent?
    c is just a number, since it does not have an "x" or "y" attached to it, it will probably be part of your y-intercept. If the letters confuse you, just replace them with a number, any number. That is what is neat about algebra, regardless of what numbers are in your equation you can solve for an answer. While you are trying to understand the concept, try to use numbers that will reduce each other, like 2x + 8y + 10 = 0 Solve for y in that equation and it will put it into slope-intercept form for you.
    3) In slope-y intercept form, what does x represent?
    Look at the graph of y = x. It is just a line through (0,0) on your graph right? y = x is actually in slope-intercept form y = 1x + 0 The slope is understood to be 1, so we leave it out and since the graph intercepts the y axis at 0, we leave that off too!
    This is so confusing. You'll get it! Hang in there! It takes practice!!

    4) Does anybody have any hints on how to learn when to use one equation rather than another, or how to solve problems with these equations? When you look at a problem you are given, try not to be overwhelmed with all the "stuff" in it. See if you can get "y" by itself using addition, subtraction, multiplication or division. Then once you get y by itself, see if it looks like one of the line equations, slope-intercept, point- slope or standard

    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