Linear Algebra from Coordinates to Equations
Two sets of coordinates are (3,8) and (2,2)
1.) Given two sets coordinates, list them so that the smallest x value comes first
example: (3,8) ; (2,2) would be listed as (2,2) ; (3,8)
2.) The first set of coordinates is (X1,Y1) the second is (X2,Y2)
3.) Using the formula (Y2 - Y1)/(X2 - X1), we obtain the gradient
8 – 2 / 3 – 2 = 6/1 = 6. This is what m equals. (m = 6)
4.) Place this value into the formula for a line y = mx + c
y = 6x + c
5.) Using only one set of coordinates, put these values into the linear equation you
obtained in 4.).
For the coordinates (2,2), you replace x = 2  y = 6(2) + c , and y = 2  2 = 6(2) + c
Which becomes; 2 = 12 + c
6.) Now we solve for c.
2 – 12 = 12 – 12 + c, which becomes – 10 = c or (c = – 10)
You can see that this also works for the other coordinates (3,8)
8 = 6(3) + c : 8 – 18 = 18 – 18 + c ; – 10 = c or (c = – 10)
7.) You can now place both values for m and c back into the formula for a line
y = mx + c.
(m = 6) and (c = – 10)
y = 6x – 10
8.) This equation can now be used for any value of x in order to determine the y value.