Problem 1 - 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. $$(4,7) \text { and }(8,10)$$

Step-by-Step Solution

Answer

The slope of the line passing through the points (4,7) and (8,10) is 3/4. The line rises.

Step 1: Identify the coordinates

Firstly, identify the coordinates of the two points. The coordinates of the first point are \( x_1=4 \) and \( y_1=7 \); the coordinates of the second point are \( x_2=8 \) and \( y_2=10 \).

Step 2: Calculate the slope

Secondly, use the formula for the slope of a line \( m = (y2-y1)/(x2-x1) \). Thus, substituting the values we have, we get \( m = (10 - 7) / (8 - 4) = 3/4 \).

Step 3: Determine the direction of the line

Finally, as the calculated slope is positive, this means that the line is rising. A positive slope indicates a line that goes up from left to right.