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.
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.
