Question

Jessica is selling books during the summer to earn money for college. She earns a commission on each shelf but has to pay her own expenses. After a month of driving from neighborhood to neighborhood and walking door-to-door she figures out that her weekly earnings are approximately a linear function of the number of door she knocks on she writes the equation of function like this: E(x)=7x-25 where X is the number of doors she knocks on during the week and E(x) is it her earnings for the week of dollars. What does the slope of Jessica's function represent

Answer 1

The very steep slope (m = 7) indicates that Jessica will have a good number of earnings if she knocks on a lot of doors in a week. Even if the function (when plotted) starts at a very low part of the graph, with each increasing number of knocks, the graph easily displays its positive slope, telling us that Jessica is able to have a hefty amount as her earnings for the week.

Answer 2

The slope represents the rate of change of earnings in a week for every unitary change in number of doors knocked. For Jessica's function, her earnings change by +7 units for every unit of door she knocks.

Explanation:

The slope of any linear function tells us the rate of increase in Y given 1 unit increase in X [note the equation as
`Y=mX+b`]. Here,
`m` is the slope.

Jessica's weekly earning function is:

`E(x)=7x-25`

Where,

• 
  `E(x)` is her weekly earnings
• 
  `x` is the number of doors she knocks

So, when comparing this to the meaning of slope stated above, we can say that the slope of Jessica's function represents the rate of change of earnings in a week for every unitary change in number of doors knocked.