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ANALTYIC GEOMETRY - Coggle Diagram

- - - - |AB| = |x-y| = |y-x|
- - - - If the line is parallel to the y-axis then m is undefined.
      - If the line is parallel to the x-axis then m = 0
  - - - Let A(x1,y1) is a point on the line ℓ and the slope of the line is m, the equation is, y-y1=m(x-x1)
      - Equation of the lines which are passing through the origin can be found by, y=mx
    - - Equation of the line with two points A(x1,y1)
        and B(x2,y2) on the line is, y-y1/x-x1 = y2-y1/ x2-x1
    - - x/a + y/b = 1
    - - ax + by + c = 0 is the standard equation of a line (a, b, and c are constants). This form is usually gotten by manipulating the slope intercept form or the two intercept forms.
    - - y=b
    - - x=a
    - - y=mx
  - - - If the equation of the line is given by + c = 0 form or y = b form, the graph of line is parallel to x-axis.
      - If the equation of the line is given ax + c = 0 form or x = a form, the graph of line is parallel
        to y-axis.
      - If the equation of the line is given ax + by = 0 form or y = mx form, the graph of line passes on origin.
    - - ax + by + c = 0 is linear equation of a line, y = mx + n is functional form of a line.
        The slope of a line given in the form y = mx + n is m.
        To find the slope of a line given in the form of ax + by + c = 0, we have the convert the equation
        to the form y = mx + n.
    - - If a1/a2 = b1/b2 dont equal c1/c2 then the lines are parallel that is d 1 // d 2 . Solution set is empty set.
      - If a1/a2 dont equal b1/b2 dont equal c1/c2 then the lines are intersecting at one point. Solution set can be find by common solution.
      - If a1/a2 = b1/b2 = c1/c2 then the lines are coincident that is d 1 = d 2. Solution set is all the real numbers.