Answer:
a) The slope of the function is 3.
c) The equation is represented by .
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:
(1)
Where:
- Slope, measured in number of pieces per minute.
- Time, measured in minutes.
- Initial number of pieces of mail that must be hand-sorted (y-intercept), measured in pieces.
- 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 and
, then the following system of linear equations is formed:
(2)
(3)
The solution of the system of equations is:
and
The slope of the function is 3.
c) By (1) and using results from a) we conclude that the equation function is:
(4)
d) The y-intercept of the function is 35.