The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#
Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.
Substituting the values from the points in the problem gives:
#m = (color(red)(-1/12) - color(blue)(5/6))/(color(red)(1/3) - color(blue)(-3/2))#
#m = (color(red)(-1/12) - color(blue)(5/6))/(color(red)(1/3) + color(blue)(3/2))#
#m = (color(red)(-1/12) - (color(blue)(2/2 xx 5/6)))/((color(red)(2/2 xx 1/3)) + (color(blue)(3/3 xx 3/2)))#
#m = (color(red)(-1/12) - color(blue)(10/12))/(color(red)(2/6) + color(blue)(9/6))#
#m = (-11/12)/(11/6)#
We can now use this rule for dividing fractions to finalize the calculation for the slope:
#(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))#
#(color(red)(-11)/color(blue)(12))/(color(green)(11)/color(purple)(12)) = (color(red)(-11) xx color(purple)(12))/(color(blue)(12) xx color(green)(11)) = -132/132 = -1#
