Question

Find an equation for the line that passes throught points (5,1) and (1,3)

Answer 1

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