Question

Can you help with did pretty please I'm stuck help just a, c ,d thanks luv.

Answer 1

a) The slope of the function is 3.

c) The equation is represented by
`n(t) = 3\cdot t + 35`.

d) The y-intercept of the function is 35.

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:

`n(t) = m\cdot t + n_(o)` (1)

Where:

`m` - Slope, measured in number of pieces per minute.

`t` - Time, measured in minutes.

`n_(o)` - Initial number of pieces of mail that must be hand-sorted (y-intercept), measured in pieces.

`n` - 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
`n(15\,min) = 80\,p` and
`n(45\,min) = 170\,p`, then the following system of linear equations is formed:

`15\cdot m + n_(o) = 80` (2)

`45\cdot m + n_(o) = 170` (3)

The solution of the system of equations is:

`m = 3` and
`n_(o) = 35`

The slope of the function is 3.

c) By (1) and using results from a) we conclude that the equation function is:

`n(t) = 3\cdot t + 35` (4)

d) The y-intercept of the function is 35.