Chapter 9.9, Problem 27PPS

(a)

To determine

The graph and which kind of function models the data

Answer to Problem 27PPS

  

The ordered pairs represent a linear function

Explanation of Solution

Given:

The cost of a long- distance telephone call depends on the length of the call

  

Concept Used:

In rectangular coordinate system any point be in the form of $\left(x,y\right)$ .

• In Quadrant I, both the coordinates of ordered pair are positive, that is, $\left(+,+\right)$ .
• In Quadrant II, first number is negative and second is positive, that is, $\left(-,+\right)$ .
• In Quadrant III, both the coordinates of ordered pair are negative, that is, $\left(-,-\right)$ .
• In Quadrant IV, first point is positive and second is negative, that is, $\left(+,-\right)$ .

In order to plot the points $\left(1,0.12\right),\left(2,0.24\right),\left(3,0.36\right),\left(4,0.48\right),\left(5,060\right),\left(6,0.72\right)$ in graph

To plot the graph of the point $\left(1,0.12\right)$ first move 2 units to the left starting from origin and then move 3 units down

To plot the graph of the point $\left(2,0.24\right)$ first move 2 units to the right starting from origin and then move 0.24 units up

To plot the graph of the point $\left(3,0.36\right)$ first move 3 units to the right starting from origin and then move 0.36 units up

To plot the graph of the point $\left(4,0.48\right)$ first move 4 units to the right starting from origin and then move 0.48 units up

To plot the graph of the point $\left(5,0.60\right)$ first move 5 units to the right starting from origin and then move 0.60 units up

To plot the graph of the point $\left(6,0.72\right)$ first move 6 units to the right starting from origin and then move 0.72 units up

The graph of the point is shown below:

  

The points are in straight line

Thus, the ordered pairs represent a linear function

(b)

To determine

The equation for the function that models the data

Answer to Problem 27PPS

The equation is given by $y=0.12x$

Explanation of Solution

Given:

  

Concept Used:

If first difference of y-values is equal, then model be linear

If second difference be equal, then the model be quadratic

If first and second differences are not equal then the model will be exponential

Calculation:

In order to the equation we take two points from the given table as shown below:

  $\begin{array}{l}\left(\mathrm{1.0.12}\right)and\left(\mathrm{2.0.24}\right)\\ m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{0.24-0.12}{2-1}\\ =\frac{0.12}{1}\\ m=0.12\end{array}$

Thus, the equation is given by $y=0.12x$

(c)

To determine

How much a 10-minute call would cost.

Answer to Problem 27PPS

The cost is $\$1.20$ .

Explanation of Solution

Calculation:

In order to find the cost 10 minute call shown below:

  $\begin{array}{l}y=0.12x\\ x=10\\ y=0.12\times 10\\ y=1.2\end{array}$

Thus, the cost is $\$1.20$ .