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[tex]\boxed{m = \frac{\Delta y}{\Delta x}}[/tex]
a) [tex]A(5,4) \ \ \ \ \ \ B(3,2) \\\\ m = \frac{\Delta y}{\Delta x} = \frac{y_{f}-y_{i}}{x_{f}-x_{i}} = \frac{2-4}{3-5} = \frac{-2}{-2} = \boxed{1}[/tex]
b) [tex]C(4,2) \ \ \ \ \ \ D(6,3) \\\\ m = \frac{\Delta y}{\Delta x} = \frac{y_{f}-y_{i}}{x_{f}-x_{i}} = \frac{3-2}{6-4} = \boxed{\frac{1}{2}}[/tex]
c) [tex]E(-2,-1) \ \ \ \ \ \ F(1,3) \\\\ m = \frac{\Delta y}{\Delta x} = \frac{y_{f}-y_{i}}{x_{f}-x_{i}} = \frac{3-(-1)}{1-(-2)} = \frac{3+1}{1+2} = \boxed{\frac{4}{3}}[/tex]
d) [tex]G(-3,2) \ \ \ \ \ \ H(6,-5) \\\\ m = \frac{\Delta y}{\Delta x} = \frac{y_{f}-y_{i}}{x_{f}-x_{i}} = \frac{-5-2}{6-(-3)} = \frac{-7}{6+3} = \frac{-7}{9} = \boxed{-\frac{7}{9}}[/tex]