To solve the equation $6 n-5=37$ , Rishi decided to construct a table of values, and then plot a graph. $\newline$ a) Complete Rishi's table of values for the equation. $\newline$ \begin{tabular}{|l|l|l|l|l|l|} $\newline$ \hline Term number $(n)$ & $1$ & $2$ & $3$ & $4$ & $5$ \\ $\newline$ \hline Term value $(6 n-5)$ & $1$ & $7$ & $13$ & $19$ & $25$ \\ $\newline$ \hline $\newline$ \end{tabular}

Full solution

Q. To solve the equation

6 n-5=37

, Rishi decided to construct a table of values, and then plot a graph.

\newline

a) Complete Rishi's table of values for the equation.

\newline

\begin{tabular}{|l|l|l|l|l|l|}

\newline

\hline Term number

(n)

1

2

3

4

5

\newline

\hline Term value

(6 n-5)

1

7

13

19

25

\newline

\hline

\newline

\end{tabular}

Understand the problem: Understand the problem. $\newline$ We need to complete a table of values for the equation $6n-5$ , where $n$ represents the term number and $6n-5$ represents the term value.
Calculate $n=1$ : Calculate the term value for $n=1$ . Using the equation $6n-5$ , we substitute $n$ with $1$ to get $6(1)-5 = 6-5 = 1$ .
Calculate $n=2$ : Calculate the term value for $n=2$ . Using the equation $6n-5$ , we substitute $n$ with $2$ to get $6(2)-5 = 12-5 = 7$ .
Calculate $n=3$ : Calculate the term value for $n=3$ . Using the equation $6n-5$ , we substitute $n$ with $3$ to get $6(3)-5 = 18-5 = 13$ .
Calculate $n=4$ : Calculate the term value for $n=4$ . Using the equation $6n-5$ , we substitute $n$ with $4$ to get $6(4)-5 = 24-5 = 19$ .
Calculate $n=5$ : Calculate the term value for $n=5$ . Using the equation $6n-5$ , we substitute $n$ with $5$ to get $6(5)-5 = 30-5 = 25$ .
Verify calculations: Verify the calculations. $\newline$ We need to ensure that the term values are correctly calculated by checking the arithmetic for each term. $\newline$ For $n=1$ , $6(1)-5 = 1$ , which is correct. $\newline$ For $n=2$ , $6(2)-5 = 7$ , which is correct. $\newline$ For $n=3$ , $6(3)-5 = 13$ , which is correct. $\newline$ For $n=4$ , $6(4)-5 = 19$ , which is correct. $\newline$ For $n=5$ , $6(5)-5 = 25$ , which is correct.