The slope of a line passing through two points A(x₁, y₁) and B(x₂, y₂) is expressed as
[tex]\begin{gathered} \text{slope = }\frac{rise}{runs}=\frac{y_2-y_1}{x_2-x_1}_{} \\ \text{where} \\ (x_1,y_1)\Rightarrow coordinate\text{ of point A} \\ (x_2,y_2)\Rightarrow coordinate\text{ of point B} \end{gathered}[/tex]
The line through the given points rises, when the slope is positive;
The line through the given points is horizontal, when the slope equals zero;
The line through the given points is vertical when the slope is undefined;
The line through the given points falls, when the slope is negative.
Given the points (3,-2) and (5, 6).
[tex]\begin{gathered} x_1=3 \\ y_1=-2 \\ x_2=5 \\ y_2=6 \end{gathered}[/tex]
thus, the slope is evaluated as
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1}=\frac{6-(-2)}{5-3}=\frac{6+2}{5-3}=\frac{8}{2} \\ \Rightarrow slope=4 \end{gathered}[/tex]
Hence, the slope passing through the points (3,-2) and (5, 6) is 4.
Since the obtained slope is positive, the line through the points (3,-2) and (5, 6) rises.
