You can write a generic line also this way:
y = mx + b
Given two points (x1,y1) and (x2,y2) on a line, the slope m of the line is:
m = (y2 - y1) / (x2 - x1)
(x1, y1) = (-1, 3)
(x2, y2) = (1, 11)
m = (11 - 3) / (1 - (-1)) = 8/2 = 4
So m = 4
The equation is now looking this way:
y = 4x + b
Choose either point and put it into the equation to find b:
(x1, y1) = (-1, 3) -----> Substituting:
3 = 4(-1) + b -----> 3 = -4 + b -----> b = 7
So the equation can be written as:
y = 4x + 7
Had we used the other point, we would have found the same value for b:
(x2, y2) = (1, 11) -----> 11 = 4(1) + b -----> b = 7
Anyway, we saw that the equation can be written as y = 4x + 7
Rewriting the equation (rearranging the terms), we get:
4x - y = -7
