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Sagot :
To complete the table using the rule [tex]\( y = \frac{1}{4} x + 1 \)[/tex], we need to calculate the value of [tex]\( y \)[/tex] for each given [tex]\( x \)[/tex] value.
Step-by-step solution:
1. For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = \frac{1}{4} \cdot 2 + 1 \][/tex]
[tex]\[ y = \frac{2}{4} + 1 \][/tex]
[tex]\[ y = 0.5 + 1 \][/tex]
[tex]\[ y = 1.5 \][/tex]
2. For [tex]\( x = 8 \)[/tex]:
[tex]\[ y = \frac{1}{4} \cdot 8 + 1 \][/tex]
[tex]\[ y = 2 + 1 \][/tex]
[tex]\[ y = 3 \][/tex]
3. For [tex]\( x = 12 \)[/tex]:
[tex]\[ y = \frac{1}{4} \cdot 12 + 1 \][/tex]
[tex]\[ y = 3 + 1 \][/tex]
[tex]\[ y = 4 \][/tex]
Thus, the completed table is as follows:
[tex]\[ \begin{array}{c|c} x & y \\ \hline 2 & 1.5 \\ 8 & 3.0 \\ 12 & 4.0 \\ \end{array} \][/tex]
This table shows the corresponding [tex]\( y \)[/tex] values for the given [tex]\( x \)[/tex] values based on the rule [tex]\( y = \frac{1}{4} x + 1 \)[/tex].
Step-by-step solution:
1. For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = \frac{1}{4} \cdot 2 + 1 \][/tex]
[tex]\[ y = \frac{2}{4} + 1 \][/tex]
[tex]\[ y = 0.5 + 1 \][/tex]
[tex]\[ y = 1.5 \][/tex]
2. For [tex]\( x = 8 \)[/tex]:
[tex]\[ y = \frac{1}{4} \cdot 8 + 1 \][/tex]
[tex]\[ y = 2 + 1 \][/tex]
[tex]\[ y = 3 \][/tex]
3. For [tex]\( x = 12 \)[/tex]:
[tex]\[ y = \frac{1}{4} \cdot 12 + 1 \][/tex]
[tex]\[ y = 3 + 1 \][/tex]
[tex]\[ y = 4 \][/tex]
Thus, the completed table is as follows:
[tex]\[ \begin{array}{c|c} x & y \\ \hline 2 & 1.5 \\ 8 & 3.0 \\ 12 & 4.0 \\ \end{array} \][/tex]
This table shows the corresponding [tex]\( y \)[/tex] values for the given [tex]\( x \)[/tex] values based on the rule [tex]\( y = \frac{1}{4} x + 1 \)[/tex].
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