Problem

Find the slope of the line passing through the points $(-6,-6)$ and $(9,-6)$.
slope:
Find the slope of the line passing through the points $(9,4)$ and $(9,-2)$.
slope:

Answer

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Answer

Final Answer: The slope of the line passing through the points \((-6,-6)\) and \((9,-6)\) is \(\boxed{0}\). The slope of the line passing through the points \((9,4)\) and \((9,-2)\) is \(\boxed{\text{undefined}}\).

Steps

Step 1 :The slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula: \[m = \frac{y_2 - y_1}{x_2 - x_1}\] where \(m\) is the slope of the line.

Step 2 :For the first question, we have the points \((-6,-6)\) and \((9,-6)\). Substituting these values into the formula, we can calculate the slope.

Step 3 :The slope of the line passing through the points \((-6,-6)\) and \((9,-6)\) is 0. This is because the y-coordinates of the two points are the same, which means the line is horizontal.

Step 4 :For the second question, we have the points \((9,4)\) and \((9,-2)\). Substituting these values into the formula, we can calculate the slope. However, we need to be careful here because the denominator will be zero, which means the slope is undefined. This is because the line is vertical.

Step 5 :The slope of the line passing through the points \((9,4)\) and \((9,-2)\) is undefined. This is because the x-coordinates of the two points are the same, which means the line is vertical.

Step 6 :Final Answer: The slope of the line passing through the points \((-6,-6)\) and \((9,-6)\) is \(\boxed{0}\). The slope of the line passing through the points \((9,4)\) and \((9,-2)\) is \(\boxed{\text{undefined}}\).

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