Problem

Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $(-5,2)$ and $(6,3)$
Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. The slope is $\square$. (Simplify your answer.)
B. The slope is undefined

Answer

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Answer

Final Answer: The slope is \(\boxed{0.09}\). The line rises.

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: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Step 2 :In this case, the two points are \((-5,2)\) and \((6,3)\). So, we can substitute these values into the formula to find the slope.

Step 3 :After executing this calculation, we get the slope of the line as approximately 0.09.

Step 4 :We can determine whether the line rises, falls, is horizontal, or is vertical based on the slope. If the slope is positive, the line rises; if the slope is negative, the line falls; if the slope is zero, the line is horizontal; if the slope is undefined (i.e., the denominator in the slope formula is zero), the line is vertical.

Step 5 :The slope of the line is approximately 0.09, which is a positive number. Therefore, the line rises from left to right.

Step 6 :Final Answer: The slope is \(\boxed{0.09}\). The line rises.

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