How to Learn the Different Equations for a Line

Step-by-Step Guide

1. 1

   Step 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)

   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. 2

   Step 2: where {x1)

   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. , Determine which Form the equation is in (the answer is in the Tips Section below). ,,,
3. 3

   Step 3: y1)} designates the Cartesian coordinates of a point on the line

4. 4

   Step 4: y} designates the Cartesian coordinates of a second point on the line

5. 5

   Step 5: and m = the slope of the line.

6. 6

   Step 6: Learn that Slope m (or sometimes a

7. 7

   Step 7: as in y = ax + b) is equal to the equation (y2 - y1) / (x2 - x1)

8. 8

   Step 8: where again

9. 9

   Step 9: y1} designates the Cartesian coordinates of a point on the line and {x2

10. 10

    Step 10: y2} designates the Cartesian coordinates of a second point on the line.

11. 11

    Step 11: Here is a simple graph of a line.

12. 12

    Step 12: Point-Slope Video: https://www.youtube.com/watch?v=ll8JouxEKOg

13. 13

    Step 13: Standard Form Video: https://www.youtube.com/watch?v=eRnSDwNqMv4

14. 14

    Step 14: Slope-Intercept Video: https://www.youtube.com/watch?v=wn-Tb2guTac#t=55

Detailed Guide

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