to get the slope of a line, we only need two points, notice, the grid is using 2 numbers per line, so the point on the bottom-left is (-6,0) and the one on the upper-right is (6,4), so let's use those points.
[tex]\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad
(\stackrel{x_2}{6}~,~\stackrel{y_2}{4})
\\\\\\
slope = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-0}{6-(-6)}\implies \cfrac{4-0}{6+6}\implies \cfrac{4}{12}\implies \cfrac{1}{3}[/tex]
