Chapter 5.7, Problem 26STP

To determine

the money in the student’s bank account in week 6

Answer to Problem 26STP

The money in the student’s bank account in week 6 is $y=\$122$

Explanation of Solution

Given info:

The balance in the student’s bank account with week wise is given below

Weekly account balance
week	1	3	4	7	9
Account balance	$35	$68	$85	$105	$136

Formula used:

Show the slope-point form as follows:

  $m=\frac{y_2-y_1}{x_2-x_1}$

Here, $m$ is the slope, $x,x_2,y_1,y_2$ are coordinate points in the graph.

Show the straight line equation as follows:

  $y=mx+c$

Here, $m$ is the slope, $x$ is the variable, and $c$ is the y-intercept.

Show the slope-intercept form as follows:

  $\left(y-y_1\right)=m\left(x-x_1\right)$

Here, $m$ is the slope, $x,y$ are the variables, and $x_1,y_1$ are the coordinate points

Calculation:

Plot the week and account balance in the graph and draw the trend line which should connect at least 3 points in the trend line to find the slope.

  

Find the slope with two points $\left(3,68\right)$ and $\left(4,85\right)$ using slope-point form as follows:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{85-68}{4-3}\\ m=\frac{17}{1}\\ m=17\end{array}$

Find the slope-intercept form using $m=17$ and coordinate point $\left(4,85\right)$ as follows:

  $\begin{array}{l}\left(y-y_1\right)=m\left(x-x_1\right)\\ \left(y-85\right)=17\left(x-4\right)\\ y-85=17x-68\\ y=17x-65+85\\ y=17x+20\end{array}$

Hence, the straight line equation is $y=17x+20$ .

Find the money $\left(y\right)$ in the student’s bank account in week 6 that is $\left(x=6\right)$ as follows:

  $\begin{array}{l}y=17x+20\\ y=\left(17\times 6\right)+20\\ y=122\end{array}$

Hence, the money $\left(y\right)$ in the student’s bank account in week 6 that is $\left(x=6\right)$ is $y=\$122$

Conclusion:

Thus, the average money $\left(y\right)$ in the student’s bank account in week 6 that is $\left(x=6\right)$ is $y=\$122$