What is the equation of the line that passes through the points
and (1/2, -1/3) 2,2/3)

the desired equation is y = (2/3)x - 2/3

Step-by-step explanation:

As we go from (1/2, -1/3) to (2,2/3), x increases by 3/2 and y increases by 1.  Hence, the slope of this line is m = rise / run = 1/(3/2), or 2/3.

Use the slope-intercept form of the equation of a straight line, y = mx + b:

Substituting 2/3 for y, 2 for x and 2/3 for m, we get:

2/3  = 2(2/3) + b.

Clear out the fractions by multiplying all three terms by 3:

2 = 4 + 3b, or -2 = 3b, or b = -2/3.

Then the desired equation is y = (2/3)x - 2/3