First find the slope, m:
2-(-1) 3
m = -------------- = --------- = 6/7
(1/2)-(-3) 3.5
Now use the slope-intercept formula:
y = mx + b
Choosing the point (1/2, 2), 2 = (6/7)(1/2) + b. Find b (the y-intercept):
14 [ 2 = (6/7)(1/2) + b ] => 28 = 6 + 14b.
Then 22 = 14b, and b = 22/14.
Then the eqn of the line is y = (6/7)X + 22/14
Mult. all terms by 14 to remove the fractions:
14y = 12x + 22
Finally, rearrange the terms: -12x + 14y - 22 = 0. This is the eqn in standard form, as requested.