Find the slope of the line through (3;1) and (3 + 4t;1 + 3t)

Question

Came from phillips exeter academy Mathematics 2 sheet.

Answer 1

The points are (3, 1) and  (3 + 4t, 1 + 3t).

(x1 , y1) = (3 , 1) and (x2, y2)= (3 +4t , 1 + 3t)

Slope formula:

 

Substitute values

Answer 2

Given two points are say (3,1) = (x1,y1)

                                    (3+4t,1+3t) = (x2,y2)

Slope of the line passing through the two points m = y2-y1/x2-x1

m = (1+3t) -1/(3+4t) -3       (simplification)

m = 1+3t-1/3+4t-3

m = 3t/4t

m = 3/4