## Calculus 8th Edition

(a) $$C=13N+900$$ The image of the graph has been added. (b) The slope of the graph is $13$. It represents the rate of change of the cost with respect to the number; for example, if the number changes by unit, then the cost changes by $13$. (c) The $C$-intercept of the graph is $900$. It represents the value of $C$ for $N=0$.
To find the equation of this linear function, $C=mN+d$, we must compute the slope, $m$, and the $C$-intercept, $d$. For the line passing through the points, $(x_1,y_1)$ and $(x_2, y_2)$, $m=\frac{y_1-y_2}{x_1-x_2}$. So we have $$m= \frac{4800-2200}{300-100}=13.$$To compute the $C$-intercept, one can put one of the given points, for example $(100,2200)$ into the line equation. So we have $$C= 13N+d \quad \Rightarrow \quad 2200=13 \cdot 100 +d \quad \Rightarrow \quad d=900.$$ So the the function is of the form $$C=13N+900.$$