Chapter 1.3, Problem 34E

To determine

Tofind:The missing values in the table given below for $y=-3x+4$ .

$x$	$y$	Change $\left(\Delta y\right)$
$1$	$?$	$?$$?$$?$
$2$	$?$
$3$	$?$
$4$	$?$

Answer to Problem 34E

The complete table for $y=-3x+4$ is shown below:

$x$	$y$	Change $\left(\Delta y\right)$
$1$	$1$	$-3$$-3$$-3$
$2$	$-2$
$3$	$-5$
$4$	$-8$

Explanation of Solution

Given information:

The equation is $y=-3x+4$ and the table is:

$x$	$y$	Change $\left(\Delta y\right)$
$1$	$?$	$?$$?$$?$
$2$	$?$
$3$	$?$
$4$	$?$

Calculation:

Substitute 1 for $x$ in the given equation.

  $\begin{array}{c}y=-3x+4\\ y=-3\times 1+4\\ y=-3+4\\ y=1\end{array}$

Substitute 2 for $x$ in the given equation.

  $\begin{array}{c}y=-3x+4\\ y=-3\times 2+4\\ y=-6+4\\ y=-2\end{array}$

Substitute 3 for $x$ in the given equation.

  $\begin{array}{c}y=-3x+4\\ y=-3\times 3+4\\ y=-9+4\\ y=-5\end{array}$

Substitute 4 for $x$ in the given equation.

  $\begin{array}{c}y=-3x+4\\ y=-3\times 4+4\\ y=-12+4\\ y=-8\end{array}$

The change $\left(\Delta y\right)$ for the values 1 and $-2$ is:

  $\begin{array}{c}\Delta y_1=y_2-y_1\\ =-2-1\\ =-3\end{array}$

The change $\left(\Delta y\right)$ for the values $-2$ and $-5$ is:

  $\begin{array}{c}\Delta y_2=y_3-y_2\\ =-5-\left(-2\right)\\ =-5+2\\ =-3\end{array}$

The change $\left(\Delta y\right)$ for the values $-5$ and $-8$ is:

  $\begin{array}{c}\Delta y_3=y_4-y_3\\ =-8-\left(-5\right)\\ =-8+5\\ =-3\end{array}$

So, the values of $\Delta y$ are $-3$ , $-3$ and $-3$ .

Therefore, the complete table is given below:

$x$	$y$	Change $\left(\Delta y\right)$
$1$	$1$	$-3$$-3$$-3$
$2$	$-2$
$3$	$-5$
$4$	$-8$