Question

The table shows the amount of money Yookyung charges customers to babysit. The table represents a linear function.

Time (h) 0 2 5 7 8
Charge ($) 5 19 40 54 61


What does the initial value mean for this function?




A. Yookyung charges $7.00 an hour to babysit.

B. Yookyung earns $40 for 5 hours of work.

C. Yookyung does not charge her customers until she has babysat for a minimum of 2 hours.

D. Yookyung charges $5 before she begins babysitting.

Answer 1

Any linear function can be written in the form y=mx+b

Here m represents the slope or we can say the difference of y over difference of x. b is the point where the graph touches the y axis .On y axis x=0 so b is the y value when x=0. The given table represents the amount of money Yookyung charges customers to babysit .

The initial value of the table is Time =0 then corresponding charge =$5

That is if Yookyung has not started the babysit as time is 0 the corresponding charge is $5 .

Option D. Yookyung charges $5 before she begins babysitting is true in this case.

Answer 2

For this case we have a function of the form:

y = mx + b

Where,

m: slope of the line

b: cutting point with the y axis.

In the context of the problem we have:

The slope of the line is the charge per hour that Yookyung charges for babysit.

The cutoff point with the y-axis is an initial fee that Yookyung charges before starting work.

The cut point with the y axis occurs when x = 0.

Therefore, observing the table we have:

b = 5

Answer:

D. Yookyung charges $5 before she begins babysitting.