Problem 4 - Introductory and Intermediate Algebra for College Students 4th

Question

Find the slope of the line passing through each 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. $$(-1,3) \text { and }(2,4)$$

Step-by-Step Solution

Answer

The slope of the line passing through the points (-1,3) and (2,4) is 1/3. Hence, the line through the points rises as the slope is positive.

Step 1: Identify The Given Points

The two points given are (-1,3) and (2,4). With these points, identify \( x_1 = -1 \), \( y_1 = 3 \), \( x_2 = 2 \), and \( y_2 = 4 \).

Step 2: Calculate the Slope

Plug these values into the slope formula \( m = \frac{y_2-y_1}{x_2-x_1} \). Here, your m (slope) will be \( m = \frac{4-3}{2 - (-1)} = \frac{1}{3} \). Unlike a number divided by zero (which would be undefined), this calculation results in a defined slope of 1/3.

Step 3: Determine the Rise or Fall

Since the slope is a positive number (1/3), it indicates that the line rises.