Chapter 9.2, Problem 37IP

a.

To determine

To find:the number of miles a whale can swim

Answer to Problem 37IP

Number of miles $2.5$ ,5,7.5 and 10

Explanation of Solution

Given information:

A whale can swim half a mile per minute and the number of mile whale can swim in 5,10,15 and 20 minutes.

Calculation:

Time(mint) $x$	$y=0.5x$	Distance(miles) $y$
5	$y=0.5\left(5\right)$	$2.5$
10	$y=0.5\left(10\right)$	5
15	$y=0.5\left(15\right)$	$7.5$
20	$y=0.5\left(20\right)$	10

b

To determine

To find:the difference between the output values

Answer to Problem 37IP

The output values increase by $2.5$

Explanation of Solution

Given information:

The input values increase by 5, does the difference between the output values increase by the same amount.

Calculation:

Time(mint) $x$	$y=0.5x$	Distance(miles) $y$
5	$y=0.5\left(5\right)$	$2.5$
10	$y=0.5\left(10\right)$	5
15	$y=0.5\left(15\right)$	$7.5$
20	$y=0.5\left(20\right)$	10

The difference between the output values is

  $\begin{array}{l}5-2.5=2.5\\ 7.5-5=2.5\\ 10-7.5=2.5\end{array}$

Hence, the output values increase by $2.5$ .

c.

To determine

To graph:a line through the points.

Explanation of Solution

Given information:

Graph the ordered pairs (time, distance).

Graph:

To graph the order pairs find the coordinate

Time(mint) $x$	$y=0.5x$	Distance(miles) $y$
5	$y=0.5\left(5\right)$	$2.5$
10	$y=0.5\left(10\right)$	5
15	$y=0.5\left(15\right)$	$7.5$
20	$y=0.5\left(20\right)$	10

Therefore, the ordered pairs (5, $2.5$ ), (10, 5), (15, $7.5$ ), and (20, 10) on a coordinate plane.

Therefore, the graph obtain as

  Interpretation: from the above graph it can be observe that, graph the order pairs(5, $2.5$ ), (10, 5),

(15, $7.5$ ) and (20, 10)

d.

To determine

To write: an equation to represent the relationship between time $x$ and numbers of miles $y$

Answer to Problem 37IP

The miles $y$ that a whale swims is one-half or $\frac{1}{2}$ of the time $x$ spent swimming so $y=\frac{1}{2}x$

Explanation of Solution

Given information:

The relationship between time $x$ and numbers of miles $y$

A whale swims is one half or $\frac{1}{2}$ of the time $x$ completes swimming to the miles $y$ that is $y=\frac{1}{2}x$ .It is a equation of relation between time $x$ and numbers of miles $y$ .