Learn the Different Equations for a Line

You will learn the 3 basic Forms for the Equation of a Line: 1) the Point-Slope Form; 2) the Standard Form; and 3) the Slope-Intercept Form in the Cartesian Plane. You will also learn how to calculate Slope in the Cartesian Plane.

Steps

The Tutorial

  1. Memorize these LINE FORMULAS and the SLOPE FORMULA:

    • Learn that the Point-Slope Form for the equation of a Line in the Cartesian Plane is: (y - y1) = m*(x - x1), where {x1), y1)} designates the Cartesian coordinates of a point on the line, {x, y} designates the Cartesian coordinates of a second point on the line, and m = the slope of the line. It does not matter which point is above or below the other point, just so long as you keep the two points separate.
    • Learn that the Standard Form for the equation of a Line in the Cartesian Plane is: Ax + By = C. Here, one finds the intercepts with the axes by setting first x equal to 0, then y = to 0.
    • Learn that the Slope-Intercept Form for the equation of a Line in the Cartesian Plane is: y = mx + b, where m = slope and b = the intercept with the y-axis.
  2. Learn that Slope m (or sometimes a, as in y = ax + b) is equal to the equation (y2 - y1) / (x2 - x1), where again, {x1, y1} designates the Cartesian coordinates of a point on the line and {x2, y2} designates the Cartesian coordinates of a second point on the line.
    • Slope Intercept Equation of vertical and horizontal lines
      • Vertical Lines
      • The Equation of a vertical line is either x = b or x = k, some constant.
      • Since a vertical line goes straight up and down, its slope is undefined. Also, the x value of every point on a vertical line is the same. Therefore, whatever the x value is, is also the value of 'b', and the line intersects the y-axis. However, if x = k, the vertical line most probably does not intersect the y-axis (unless k=b).
    • Horizontal Lines
      • The equation of a horizontal line is y = b where b is the y-intercept.
      • Since the slope of a horizontal line is 0, the general formula for the slope-intercept form equation, y = mx + b, becomes y= 0x +b, or y = b. Also,since the line is horizontal, every point on that line has the exact same y value. This y-value is therefore also the y-axis intercept.
  3. Here is a simple graph of a line. Determine which Form the equation is in (the answer is in the Tips Section below).



Video Assistance

  1. Point-Slope Video: https://www.youtube.com/watch?v=ll8JouxEKOg
  2. Standard Form Video: https://www.youtube.com/watch?v=eRnSDwNqMv4
  3. Slope-Intercept Video: https://www.youtube.com/watch?v=wn-Tb2guTac#t=55

Tips

  • The pictured simple graph line formula is in STANDARD FORM, Ax + By = C.

References

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