Explanation:
what do you mean by "rule" ?
the line equation (in slope-intercept form ? or any other ?) ?
or only the slope of the line ?
I assume you need the slope-intercept line equation.
this looks like
y = ax + b
"a" is the slope of the line, "b" is the y-intercept (the y value when x = 0).
"b" we know already from the specified intercept points : 5.5
the slope of a line is simply the ratio
(y coordinate change / x coordinate change)
when going from one point on the line to another.
and the axis-intercept points are points on the line too. so, we can use them.
so, we see
x changes by +3.667
(= 3 2/3 = 3×3/3 + 2/3 = (3×3 + 2)/3 = 11/3)
from -3.667 to 0.
y changes by +5.5
(= 5 1/2 = 5×2/2 + 1/2 = (5×2 + 1)/2 = 11/2)
from 0 to 5.5
the slope is therefore
5.5 / 3.667 = 11/2 / 11/3 = 11/2 × 3/11 = 3×11 / 2×11 = 3/2
and so, the line equation is
y = 3/2 x + 5.5
or
y = 3/2 x + 11/2 = 1/2 × (3x + 11)