Answer:
The correct option is;
[tex]8.3 = -0.5 \times \left | x -5 \right | + 9[/tex]
Step-by-step explanation:
The coordinates of the roof are;
Starting point, = (1, 7)
Maximum height = (5, 9)
Maximum range = (9, 7)
The slope of the left portion of the roof = (9 - 7)/(5 - 1) = 0.5
The equation of the left portion of the roof is given as follows;
y - 9 = 0.5 × (x - 5)
y = 0.5 × (x - 5) + 9
The slope of the right portion of the roof = (7 - 9)/(9 - 5) = -0.5
The equation of the right portion of the roof is given as follows;
y - 9 = -0.5 × (x - 5)
y = -0.5 × (x - 5) + 9
However, when x < 5, we have;
[tex]0.5 \times \left | x -5 \right |= -0.5 \times \left | x -5 \right |[/tex]
[tex]\therefore y = 0.5 \times \left | x -5 \right | + 9 = -0.5 \times \left | x -5 \right | + 9 = 0.5 \times \left ( x -5 \right ) + 9[/tex]
When x > 5, we have;
[tex]0.5 \times \left | x -5 \right |> -0.5 \times \left | x -5 \right |[/tex]
[tex]\therefore y = -0.5 \times \left | x -5 \right | + 9 = -0.5 \times \left ( x -5 \right ) + 9[/tex]
Therefore, the equation that applies to both the left and right portion of the roof is [tex]y = -0.5 \times \left | x -5 \right | + 9[/tex]
Which gives the correct option as follows;
[tex]y = 8.3 = -0.5 \times \left | x -5 \right | + 9[/tex]
