Let's complete the table using the equation \( y = \frac{1}{2}x - 5 \).
We will calculate \( y \) for each \( x \) value provided:
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For \( x = -10 \): \[ y = \frac{1}{2}(-10) - 5 = -5 - 5 = -10 \]
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For \( x = -2 \): \[ y = \frac{1}{2}(-2) - 5 = -1 - 5 = -6 \]
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For \( x = 0 \): \[ y = \frac{1}{2}(0) - 5 = 0 - 5 = -5 \]
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For \( x = 6 \): \[ y = \frac{1}{2}(6) - 5 = 3 - 5 = -2 \]
Now we have:
\[ \begin{array}{|c|c|} \hline x & y \ \hline -10 & -10 \ -2 & -6 \ 0 & -5 \ 6 & -2 \ \hline \end{array} \]
Table Completion
So the completed table is:
\[ \begin{array}{|c|c|} \hline x & y \ \hline -10 & -10 \ -2 & -6 \ 0 & -5 \ 6 & -2 \ \hline \end{array} \]
Graphing the Function
To graph the function \( y = \frac{1}{2}x - 5 \):
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Plot the points from the table:
- Point 1: \((-10, -10)\)
- Point 2: \((-2, -6)\)
- Point 3: \((0, -5)\)
- Point 4: \((6, -2)\)
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Draw a straight line through the points, since this is a linear function.
The slope of the line is \( \frac{1}{2} \), meaning for every 2 units you move in the x direction, you move up 1 unit in the y direction.
Graphing Instructions:
- Start at the y-intercept, which is \( (0, -5) \).
- From there, use the slope to find other points.
- Draw the line that connects the points, and continue it in both directions.
This graph will represent the linear function \( y = \frac{1}{2}x - 5\). If you need a specific visual graph, please use graphing software or graph paper to plot the points and the line.