Find an equation in standard form of the line containing the given pair of points.

I will assume Gino's anser is correct but it is not in standard form.

$$\\y = 5x -7/4\\
4y=20x-7\\
7=20x-4y\\
20x-4y=7$$

First, find the slope:  m  =  (y2 - y1) / (x2 - x1)

x1 = 1/4  y1 = -1/2  x2 = 3/4  y2 = 2     ---> 

m  =  (2 - -1/2) / (3/4 - 1/4)   =   (5/2) / (1/2)   =  5

Use the point-slope form for the equation of the line:    y - y1  =  m(x - x1)

y - -1/2  =  5(x - 1/4)     --->     y + 1/2  =  5x - 5/4     --->     y  =  5x -7/4