Tamara was asked to write an example of a linear functional relationship. She wrote this example:

Question

Tamara was asked to write an example of a linear functional relationship. She wrote this example:
-my babysitting service and initial 5 dollars fee plus an additional $6.50 per hour. complete the table below to show the babysitting rate for different numbers of total hours. Then write a linear equation in the form y=mx+b that represents this relationship where m is the slope and b is the y-intercept

GPT-4o mini · Answer

Let's start by identifying the elements of Tamara's example. The initial fee (y-intercept) is $5, and the rate per hour (slope) is $6.50.

To summarize:

The initial fee (b) = $5
The rate per hour (m) = $6.50

The linear equation representing this relationship can be written as:

\[ y = 6.50x + 5 \]

Where:

$ y $ is the total cost of babysitting,
$ x $ is the number of hours babysat.

Next, let's complete the table for different numbers of total hours (x):

| Hours (x) | Total Cost (y = 6.50x + 5) | |-----------|-----------------------------| | 0 | $ 6.50(0) + 5 = 5 $ | | 1 | $ 6.50(1) + 5 = 11.50 $ | | 2 | $ 6.50(2) + 5 = 18 $ | | 3 | $ 6.50(3) + 5 = 24.50 $ | | 4 | $ 6.50(4) + 5 = 31 $ | | 5 | $ 6.50(5) + 5 = 37.50 $ |

Now, let’s provide the completed table:

| Hours (x) | Total Cost (y) | |-----------|-----------------| | 0 | 5 | | 1 | 11.50 | | 2 | 18 | | 3 | 24.50 | | 4 | 31 | | 5 | 37.50 |

Thus, to have a complete summary, the linear relationship is represented by the equation $ y = 6.50x + 5 $ and the table above shows the total cost for varying hours of service.