Questions: Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line through the points is increasing, decreasing, horizontal, or vertical. (-8, -5) and (7, 3) A. 1/3 rises B. -8/15 falls C. 1/2 falls D. 8/15 rises

Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line through the points is increasing, decreasing, horizontal, or vertical.
(-8, -5) and (7, 3)

A. 1/3 rises

B. -8/15 falls

C. 1/2 falls

D. 8/15 rises

Transcript text: MA 0800 - 01 Intermediate Algebra Quiz: Quiz 4 (2.1, 2.2, 2.3) Question 4 of 7 Question list Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10 Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line through the points is increasing, decreasing, horizontal, or vertical. (-8, -5) and (7, 3) A. $\frac{1}{3}$ rises B. -$\frac{8}{15}$ falls C. $\frac{1}{2}$ falls D. $\frac{8}{15}$ rises

Solution

Solution Steps

To find the slope of the line through two points, use the formula for the slope $ m $ which is $(y_2 - y_1) / (x_2 - x_1)$. Substitute the given points into this formula to calculate the slope. Once the slope is determined, analyze its sign: a positive slope indicates the line is increasing (rises), a negative slope indicates the line is decreasing (falls), a zero slope indicates a horizontal line, and an undefined slope (division by zero) indicates a vertical line.

Step 1: Calculate the Slope

To find the slope $ m $ of the line through the points $(-8, -5)$ and $ (7, 3) $, use the slope formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - (-5)}{7 - (-8)} = \frac{3 + 5}{7 + 8} = \frac{8}{15} \]

Step 2: Determine the Nature of the Line

The slope $ m = \frac{8}{15} $ is positive, which indicates that the line is increasing. Therefore, the line through the points $(-8, -5)$ and $ (7, 3) $ rises.