If the pitch is 8, it means the roof raises 8 ft. per each horizontal 12 ft.
Since slope, m, is defined as the rise/run; then m = 8/12.
Simplifying, we obtain a slope m = 2/3
In order to write the line of the roof as an equation, let's assume
that the roof line starts at the origin (0, 0); it rises 8 units for
every 12 it advances; up to the point (12, 8). At this point, the roof
descends at the same rate until it reaches the point (0, 24). We need
to set two equations with the given constraints:
y = mx + b since the roof ascend from (0, 0) up until (8, 12) we use a positive slope:
y = 2/3x + b If we use (0, 0) to define b, then the equation of this section of the roof will be:
y = 2/3x 〈0 ≤ x ≥ 12〉
At (12, 8) the roof starts descending at the same rate, then we use the negative slope m = -2/3:
y = -2/3x + b Now, let's use (12, 8) to define b:
8 = (-2/3)(12) + b Simplifying, we obtain b = 16, ∴ the equation of this section of the roof will be:
y = -2/3x + 16 〈12 ≤ x ≤ 24〉
