Answer:
[tex]c(t)=-18t+212[/tex].
Step-by-step explanation:
We have been given that 4 days I have 140 copies of a book, 9 days I only have 50 left. We are asked to write an equation [tex]c(t)=my+b[/tex], where c is number of copies still on hand and t days being available.
We have two points on line (4,140) and (9,50). Now, we will use these points to find slope as:
[tex]m=\frac{140-50}{4-9}[/tex]
[tex]m=\frac{90}{-5}[/tex]
[tex]m=-18[/tex]
Now, we will use point-slope form of equation [tex]y-y_1=m(x-x_1)[/tex] and substitute [tex]m=-18[/tex] and coordinates of point (9,50) as:
[tex]y-50=-18(x-9)[/tex]
[tex]y-50=-18x+162[/tex]
[tex]y-50+50=-18x+162+50[/tex]
[tex]y=-18x+212[/tex]
Therefore, our required equation would be [tex]c(t)=-18t+212[/tex].
