Answer :
a) C = 14w + 48
b) slope =
Explanation:
A) Let C represent the cost of the waste
w represent the number of kilograms of waste
when cost = $1448, the amount of waste = 100kg
(w, C) = (100, 1448)
when cost = $2498, the amount of waste = 175kg
(w, C) = (175, 2498)
we need to find the slope of the points we were given
Slope formula is given as:
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ In\text{ this case: }m\text{ = }\frac{C_2-C_1}{w_2-w_1} \\ \end{gathered}[/tex][tex]\begin{gathered} w_1=100,C_1=1448,w_2=175,C_2\text{ = 2}498 \\ m\text{ = }\frac{2498-1448}{175-100}\text{ = }\frac{1050}{75} \\ m\text{ = slope = 14} \end{gathered}[/tex][tex]\begin{gathered} Lin\text{ear equation is given as:} \\ y\text{ =mx + b};\text{ }m\text{ = slope, b = y-intercept} \\ C\text{ = mw + b} \\ m\text{ = slope, b = y-intercept} \\ To\text{ get b, we will use the slope and any of the points:} \\ point\colon(100,\text{ 1448) = (w, C)} \\ 1448\text{ = 14(100) + b} \\ b\text{ = 1448 -1400} \\ b\text{ = 48} \end{gathered}[/tex][tex]\begin{gathered} \text{The linear function becomes:} \\ C\text{ = 14w + 48} \end{gathered}[/tex]B) slope = 14
Slope = cost/amount of waste
In units, we are dividing the dollar by the kilogram = $/kg
The units of the slope is dollars per kilogram (option D)
C) Vertical intercpet is the y -intercept
From our calculation, y-intercept is = b = 48
Hence, the vertical intercept is 48
The y-intercept is the intial value or initial cost of the waste. This is the cost when the kilogram of waste is zero
C = 14w + 48
w = 0
C = 14(0) + 48
C =48
Since the unit of C is dollars. Then the unit of the intercept will also be in dollars (option D).