Answer:
a) The slope of the function is 3.
c) The equation is represented by [tex]n(t) = 3\cdot t + 35[/tex].
d) The y-intercept of the function is 35.
Step-by-step explanation:
a) According to the statement, we must assume that number of pieces of mail that must be hand-sorted (dependent variable) is represented by a linear function in terms of time (independent variable). That is:
[tex]n(t) = m\cdot t + n_{o}[/tex] (1)
Where:
[tex]m[/tex] - Slope, measured in number of pieces per minute.
[tex]t[/tex] - Time, measured in minutes.
[tex]n_{o}[/tex] - Initial number of pieces of mail that must be hand-sorted (y-intercept), measured in pieces.
[tex]n[/tex] - Current number of pieces of mail that must be hand-sorted, measured in pieces.
From Geometry, we know that a line can be formed by know two distinct points. If we know that [tex]n(15\,min) = 80\,p[/tex] and [tex]n(45\,min) = 170\,p[/tex], then the following system of linear equations is formed:
[tex]15\cdot m + n_{o} = 80[/tex] (2)
[tex]45\cdot m + n_{o} = 170[/tex] (3)
The solution of the system of equations is:
[tex]m = 3[/tex] and [tex]n_{o} = 35[/tex]
The slope of the function is 3.
c) By (1) and using results from a) we conclude that the equation function is:
[tex]n(t) = 3\cdot t + 35[/tex] (4)
d) The y-intercept of the function is 35.
