Use the drawing tools to plot the correct answers on the graph.

Consider this linear function:
[tex]\[ y = \frac{1}{2} x + 1 \][/tex]

Plot all ordered pairs for the values in the domain:
[tex]\[ D: \{-8, -4, 0, 2, 6\} \][/tex]

[tex]\[
\begin{tabular}{|c|c|}
\hline
Drawing Tools & \\
\hline
Select & \\
\hline
Point & \\
\hline
\end{tabular}
\][/tex]

Click on a tool to begin drawing.



Answer :

Sure! Let's go through the steps needed to plot the ordered pairs for the given linear function, [tex]\( y = \frac{1}{2} x + 1 \)[/tex], with the domain [tex]\( D: \{-8, -4, 0, 2, 6\} \)[/tex].

Step-by-Step Solution:

1. Identify the formula: The given linear function is [tex]\( y = \frac{1}{2} x + 1 \)[/tex].

2. Apply the domain values to the function:

- For [tex]\( x = -8 \)[/tex]:
[tex]\( y = \frac{1}{2}(-8) + 1 = -4 + 1 = -3 \)[/tex]
Hence, the ordered pair is [tex]\((-8, -3)\)[/tex].

- For [tex]\( x = -4 \)[/tex]:
[tex]\( y = \frac{1}{2}(-4) + 1 = -2 + 1 = -1 \)[/tex]
Hence, the ordered pair is [tex]\((-4, -1)\)[/tex].

- For [tex]\( x = 0 \)[/tex]:
[tex]\( y = \frac{1}{2}(0) + 1 = 0 + 1 = 1 \)[/tex]
Hence, the ordered pair is [tex]\((0, 1)\)[/tex].

- For [tex]\( x = 2 \)[/tex]:
[tex]\( y = \frac{1}{2}(2) + 1 = 1 + 1 = 2 \)[/tex]
Hence, the ordered pair is [tex]\((2, 2)\)[/tex].

- For [tex]\( x = 6 \)[/tex]:
[tex]\( y = \frac{1}{2}(6) + 1 = 3 + 1 = 4 \)[/tex]
Hence, the ordered pair is [tex]\((6, 4)\)[/tex].

3. List all ordered pairs: The list of ordered pairs is:
[tex]\[ (-8, -3), (-4, -1), (0, 1), (2, 2), (6, 4) \][/tex]

4. Plot these ordered pairs on a graph:

- To plot these points correctly, you need graphing tools or graph paper.
- Mark each point on the graph according to its coordinates:
- Point at [tex]\((-8, -3)\)[/tex]
- Point at [tex]\((-4, -1)\)[/tex]
- Point at [tex]\((0, 1)\)[/tex]
- Point at [tex]\((2, 2)\)[/tex]
- Point at [tex]\((6, 4)\)[/tex]

Once you mark these points on the graph, you will see that they all lie on the straight line defined by the function [tex]\( y = \frac{1}{2} x + 1 \)[/tex].

That's the detailed solution you need to follow in order to plot the given linear function with the specified domain values.