Chapter SH, Problem 2.10MPS

(a)

To determine

To calculate:To make a function table of possible values of $x$ and $y$ , where $x$ represents the number of goals in the first period and $y$ represents the number of goals in the second period when the total goals in the first two periods are $5$ .

Answer to Problem 2.10MPS

The functional table is:

$x$	$0$	$1$	$2$	$3$	$4$	$5$
$y$	$5$	$4$	$3$	$2$	$1$	$0$

Explanation of Solution

Given information:

  $x$ represents the number of goals in the first period and $y$ represents the number of goals in the second period when the total goals in the first two periods are $5$ .

Calculation:

The $x$ represents the number of goals in the first period and $y$ represents the number of goals in the second period when the total goals in the first two periods are $5$ .

Thus, the equation that represents the above explanation will be

  $x+y=5$

Now, substituting the values of $x$ and $y$ , so that the sum of goals is $5$ ,we have:

  $\begin{array}{l}x=0,y=5\\ x=1,y=4\\ x=2,y=3\\ x=3,y=2\\ x=4,y=1\\ x=5,y=0\end{array}$

Thus, the functional table is:

$x$	$0$	$1$	$2$	$3$	$4$	$5$
$y$	$5$	$4$	$3$	$2$	$1$	$0$

Conclusion:

The functional table is:

$x$	$0$	$1$	$2$	$3$	$4$	$5$
$y$	$5$	$4$	$3$	$2$	$1$	$0$

(b)

To determine

To calculate: To graph the ordered pairs and describe the graph.

Answer to Problem 2.10MPS

The graph is:

The graph is a straight line.

Explanation of Solution

Given information:

  $x$ represents the number of goals in the first period and $y$ represents the number of goals in the second period when the total goals in the first two periods are $5$ .

Calculation:

From Sub-part (a), the function table that represents the total goals in the first two periods is given by:

$x$	$0$	$1$	$2$	$3$	$4$	$5$
$y$	$5$	$4$	$3$	$2$	$1$	$0$

Thus, plotting the above points on a graph, we have:

From the points plotted on the above graph, the graph is a straight line.

Conclusion:

The graph is:

The graph is a straight line.