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  • Coordinate systems are formed by the intersection of two lines called axes. The horizontal axis is called x, while the vertical axis is called y.
  • Coordinate points are named by an ordered pair (x,y).
  • Slope: defined as the vertical change divided by the horizontal change (or RISE/RUN)
    Slope formula: y2 – y1
    x2 – x1
  • Types of slopes
    1. Slopes that rise from left to right are positive.
    2. Slopes that fall from left to right are negative.
    3. Horizontal lines have a slope of 0.
    4. Vertical lines have slopes that are undefined.

     

  • Slope-intercept form of an equation: y = mx + b where m = slope and b = y-intercept
  • Standard form of an equation: Ax + By + C = 0 where A,B,C are integers and A>0.
  • Parallel lines have the same slopes while perpendicular lines have negative reciprocal slopes. (e.g. slope of line 1 = 3, slope of line 2 = 3, slope of line 3 = -1/3; therefore line 1 and 2 are parallel, line 1 and 3 are perpendicular)
  • The distance between any two points P1(x1,y1) and P2(x2,y2) is given by this formula:
  • When M is the midpoint of a line segment having endpoints P1(x1,y1) and P2(x2,y2), the coordinates of M are:
  • To find the equation of a line given the slope and 1 point: (e.g. find the slope of the line with slope 2/3 and point A(3,4)
    1. Pick some other point on the line and call it (x,y)
    2. Use the given point and (x,y) with the slope in the slope formula:
    (y-4)
    = 2
    (x-3)
    3
    3. Cross multiply and simplify:
    2(x-3)
    = 3(y-4)
    2x – 6
    = 3y – 12
    4. Rearrange into standard form of equation:
    2x – 3y + 6
    = 0
  • To find the equation of a line given two points: (e.g. find the equation of the line with points A(5,-4) and B(3,2))
    1. Find the slope using the given points and the slope formula

    (2
    – -4)

    (3 – 5)

    = _6
    -2
    =-3
    2. Follow the above steps 1 – 4 using one of the given points and the slope.