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)(0) - color(blue)(1/3))/(color(red)(-1/2) - color(blue)(-1/4)) = (color(red)(0) - color(blue)(1/3))/(color(red)(-1/2) + color(blue)(1/4)) = (-color(blue)(1/3))/((2/2 xx color(red)(-1/2)) + color(blue)(1/4)) =#
#(-color(blue)(1/3))/(color(red)(-2/4) + color(blue)(1/4)) = (-color(blue)(1/3))/(color(red)(-1/4)) = (-color(red)(4) xx color(blue)(1))/(-color(blue)(3) xx color(red)(1)) = (-4)/-3 = 4/3#
