Chapter 1, Problem 11STP

(a)

To determine

To complete: The table for each value of $x$ .

Answer to Problem 11STP

Thecomplete table shown in table (1).

Explanation of Solution

Given information:

The given equation is $y=2\left(4+x\right)$ .

Calculation:

Find the value of $y$ for $x=1$ .

  $\begin{array}{c}y=2\left(4+1\right)\\ =2\left(5\right)\\ =10\end{array}$

Find the value of $y$ for $x=2$ .

  $\begin{array}{c}y=2\left(4+2\right)\\ =2\left(6\right)\\ =12\end{array}$

Find the value of $y$ for $x=3$ .

  $\begin{array}{c}y=2\left(4+3\right)\\ =2\left(7\right)\\ =14\end{array}$

Find the value of $y$ for $x=4$ .

  $\begin{array}{c}y=2\left(4+4\right)\\ =2\left(8\right)\\ =16\end{array}$

Find the value of $y$ for $x=5$ .

  $\begin{array}{c}y=2\left(4+5\right)\\ =2\left(9\right)\\ =18\end{array}$

Find the value of $y$ for $x=6$ .

  $\begin{array}{c}y=2\left(4+6\right)\\ =2\left(10\right)\\ =20\end{array}$

The complete table will be as follows.

x	y
$1$	$10$
$2$	$12$
$3$	$14$
$4$	$16$
$5$	$18$
$6$	$20$

Table (1)

(b)

To determine

To plot: The points from the table and explain about the graph.

Explanation of Solution

Given information:

The table is as follows.

x	y
$1$	$10$
$2$	$12$
$3$	$14$
$4$	$16$
$5$	$18$
$6$	$20$

Graph:

Plot the graph as shown below.

  

Figure (1)

Interpretation:

From the graph, it can be seen that the points represent a straight line.

Therefore, the graph is shown in figure (1) and points represent a straight line.

(c)

To determine

To make: The conjecture about the relationship between the change in $x$ and the change in $y$ .

Answer to Problem 11STP

When $x$ increases by 1 unit the $y$ increases by $2$ units.

Explanation of Solution

Given information:

The table is as follows.

x	y
$1$	$10$
$2$	$12$
$3$	$14$
$4$	$16$
$5$	$18$
$6$	$20$

Calculation:

From the table it can be seen that when $x$ increases by 1 unit the $y$ increases by $2$ units.