Given:
a) the slope of the linear function C is calculated as,
Consider two points ( 5,51.25) and ( 10, 52.5).
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)=\mleft(5,51.25\mright) \\ (x_2,y_2)=(10,52.5) \\ m=\frac{52.5-51.25}{10-5} \\ m=\frac{1.25}{5} \\ m=0.25 \end{gathered}[/tex]
Slope is 0.25.
b) Given that x represents cup of coffee per day.
For 0 cup of coffee, cost is $50 . that is fixed cost also known as y-intercept.
The slope-intercept form of equation of line is,
[tex]\begin{gathered} y=mx+b \\ m=0.25,b=50 \\ y=0.25x+50 \\ C=0.25x+50 \end{gathered}[/tex]
For x=200,
[tex]\begin{gathered} C=0.25(200)+50 \\ C=100 \end{gathered}[/tex]
Answer: C(200)=100
