The equation of a line in slope-intercept form is: y=mx + b
where m = slope of the line (that is, rise over run)
b = y-intercept of the line (the place where x=0)
The line y=4 is really y=(0)x + 4.
The slope is 0, so it is a horizontal line (it doesn't rise or fall as x increases).
The line crosses the y axis (the y-intercept, where x=0) at y=4. The point (0,4).
Since it is a horizontal line, y = 4 no matter what value x has.
now, y = x/2 is the same as y = (1/2)x + 0 m = slope = 1/2 and y-intercept = 0
y = (2/3)x + 0 has a y-intercept of (0,0) and rises 2 values of y for every 3 value increases in x.
Two points determine a line. Connect the dots and keep going in each direction.
So, the points (0,0) and (2,1) form the line y=(1/2)x
and the points (0.,0) and (3.2) form the line y = (2/3)x