Step 1. The two points that cross through the line are:
[tex]\begin{gathered} (-8,14) \\ (6,20) \end{gathered}[/tex]And we are required to find the slope as a simplified fraction.
Step 2. For reference, we will label the points as (x1,y1) and (x2,y2):
[tex](-8,14)\rightarrow x_1=-8,\text{ }y_1=14[/tex][tex](6,20)\rightarrow x_2=6,\text{ }y_2=20[/tex]Step 3. To find the slope 'm' we use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substituting the known values:
[tex]m=\frac{20-14}{6-(-8)}[/tex]Step 4. Solving the operations:
[tex]\begin{gathered} m=\frac{6}{6+8} \\ m=\frac{6}{14} \end{gathered}[/tex]Simplifying the fraction by dividing both numbers by 2:
[tex]m=\frac{6}{14}=\boxed{\frac{3}{7}}[/tex]The slope is 3/7.
Answer:
[tex]\frac{3}{7}[/tex]