For these equations, we are going to use the slope formula, as defined below ([tex] m [/tex] is slope and [tex] (x_1, y_1) [/tex] and [tex] (x_2, y_2) [/tex] are coordinate points):
[tex] m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
We can simply "plug in" the coordinates we are given:
[tex] m_1 = \dfrac{1 - 4}{5 - (-1)} = \dfrac{1-4}{5+1} = - \dfrac{3}{6} = - \dfrac{1}{2} [/tex]
[tex] m_2 = \dfrac{10 - 4}{0 - (-3)} = \dfrac{10-4}{3} = \dfrac{6}{3} = 2 [/tex]
Our answers are:
[tex] \boxed{m_1 = - \dfrac{1}{2}} [/tex]
[tex] \boxed{m_2 = 2} [/tex]
