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. \[ (-5,1) \text { and }(3,4) \] 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. Indicate whether the line through the points, rises, falls, is horizontal, or is vertical. A. The line is horizontal. B. The line falls from left to right. C. The line is vertical. D. The line rises from left to right.
Solution
Step 1 ：Given two points (-5,1) and (3,4), we can find the slope of the line passing through these points using the formula: \(m = \frac{y2 - y1}{x2 - x1}\)
Step 2 ：Substitute the given points into the formula: \(m = \frac{4 - 1}{3 - (-5)}\)
Step 3 ：Simplify the expression to find the slope: \(m = \frac{3}{8} = 0.375\)
Step 4 ：Since the slope is positive, the line rises from left to right.
Step 5 ：Final Answer: The slope is \(\boxed{0.375}\). The line rises from left to right.
