1 Answer

The equation can be found by using the "two point formula" in co-ordinate geometry as follows:

( y - y1 ) / ( x - x1 ) = ( y2 - y1 ) / ( x2 - x1 ) where x1 and y1 are the co-ordinates of one point and x2 and y2 are the co-ordinates of the other point.

In this problem, x1 = 1/4 , y1 = 1/2 , x2 = 3/4 , y2 = 3

Substitute these values in the two point formula.

( y - 1/2 ) / ( x - 1/4 ) = ( 3 - 1/2 ) / ( 3/4 - 1/4 )

( y - 1/2 ) / ( x - 1/4 ) = (5/2) / (1/2) = 5

( y - 1/2 ) = 5 ( x - 1/4 )

y - 1/2 = 5x - 5/4

y = 5x - 5/4 + 1/2

y = 5x - 3/4

In this equation, m = 5 and b = -3/4  ( the gradient is 5 and the line intersects the y-axis

at -3/4 ).  Please let me know if you have any further questions regarding this problem.