Intermediate Algebra, Chapter 3, 3.2, Section 3.2, Problem 28

(a) Determine the slope of the ling through the pair of points $(-3,-3)$ and $(5,6)$.

Let $(-3,-3) = (x_1, y_1)$ and $(5,6) = (x_2,y_2)$ in the slope formula

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - (-3)}{5-(-3)} = \frac{9}{8}$

The slope is $\displaystyle \frac{9}{8}$.

(b) Based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical.

Based on the slope, the line through points $(-3,-3)$ and $(5,6)$ rises from left to right.