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4) Given [tex]$t = d - 2$[/tex], starting with [tex]$d = 2$[/tex] up to [tex]$d = 10$[/tex]:

[tex]\[
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}
\hline
$d$ & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
\hline
$t$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
\hline
\end{tabular}
\][/tex]

The pairs of values are:
[tex]\[
\{(2, 0), (3, 1), (4, 2), (5, 3), (6, 4), (7, 5), (8, 6), (9, 7), (10, 8)\}
\][/tex]

Activity 3.1(b):

In the coming section, the number of spaces ([tex]$y$[/tex]) in October is related to the number of centers ([tex]$x$[/tex]) employed by the relation [tex]$y = ax$[/tex]. Starting with [tex]$x = 1$[/tex] up to [tex]$x = 12$[/tex], complete the table for the values of [tex]$x$[/tex].

b) Given the relation [tex]$y = 5x + 7$[/tex] and values of [tex]$x$[/tex] as [tex]$0, 1, 2, 3, 4, 5, and 6$[/tex], complete the table for the values of [tex]$x$[/tex].

[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
0 & 7 \\
1 & 12 \\
2 & 17 \\
3 & 22 \\
4 & 27 \\
5 & 32 \\
6 & 37 \\
\hline
\end{tabular}
\][/tex]



Answer :

GinnyAnswer
Let's start by addressing the relationship given in part (b) of the problem:

We are given the equation [tex]\( y = 5x + 7 \)[/tex] and a set of values for [tex]\( x \)[/tex]. The task is to find the corresponding values of [tex]\( y \)[/tex] for each given [tex]\( x \)[/tex].

The values of [tex]\( x \)[/tex] provided are [tex]\( 0, 1, 2, 3, 4, 5, \)[/tex] and [tex]\( 6 \)[/tex].

Let's calculate [tex]\( y \)[/tex] for each value of [tex]\( x \)[/tex] step-by-step:

1. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 5(0) + 7 = 0 + 7 = 7 \][/tex]

2. For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 5(1) + 7 = 5 + 7 = 12 \][/tex]

3. For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 5(2) + 7 = 10 + 7 = 17 \][/tex]

4. For [tex]\( x = 3 \)[/tex]:
[tex]\[ y = 5(3) + 7 = 15 + 7 = 22 \][/tex]

5. For [tex]\( x = 4 \)[/tex]:
[tex]\[ y = 5(4) + 7 = 20 + 7 = 27 \][/tex]

6. For [tex]\( x = 5 \)[/tex]:
[tex]\[ y = 5(5) + 7 = 25 + 7 = 32 \][/tex]

7. For [tex]\( x = 6 \)[/tex]:
[tex]\[ y = 5(6) + 7 = 30 + 7 = 37 \][/tex]

Now, let's compile the results into a table for better clarity:

[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 0 & 7 \\ 1 & 12 \\ 2 & 17 \\ 3 & 22 \\ 4 & 27 \\ 5 & 32 \\ 6 & 37 \\ \hline \end{array} \][/tex]

So, the table representing the values of [tex]\( y \)[/tex] corresponding to each given value of [tex]\( x \)[/tex] according to the equation [tex]\( y = 5x + 7 \)[/tex] is complete and correct.

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