Answer
0.25
When x is 200, C is 90
Explanation
The given function: y = C(x)
Using the following coordinates from the given table;
(5, 41.25) and (10, 42.5)
The slope of the line corresponding to the graph y = C(x) is calculated as shown below
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{42.5-41.25}{10-5} \\ m=\frac{1.25}{5} \\ m=0.25 \\ \text{That is the slope is 0.25} \end{gathered}[/tex]
To get the value of C, when x is 200 in the chart, we shall calculate it as follows
[tex]\begin{gathered} \text{Equation of a linear graph is:} \\ y=mx+c \\ \Rightarrow C=mx+c \\ \text{Where;} \\ m\text{ is the slope = 0.25} \\ x\text{ is the independent variable} \\ c\text{ is the C-intercept} \\ C\text{ is the dependent variable} \end{gathered}[/tex]
To get c, use (5, 41.25)
[tex]\begin{gathered} 41.25=0.25(5)+c \\ 41.25=1.25+c \\ c=41.25-1.25 \\ c=40 \end{gathered}[/tex]
Therefore,
C = 0.25(200) + 40
C= 50 + 40
C = 90
