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 two points from the problem gives:
#m = (color(red)(3/4) - color(blue)(1/8))/(color(red)(1/2) - color(blue)(1/4))#
Next, put the fractions in the numerator and the fractions in the denominator over common denominators so they can be subtracted:
#m = (color(red)((2/2 xx 3/4) - color(blue)(1/8))/(color(red)(2/2 xx 1/2) - color(blue)(1/4))#
#m = (color(red)(6/8) - color(blue)(1/8))/(color(red)(2/4) - color(blue)(1/4)) = (5/8)/(1/4)#
Now, use the rule for dividing fractions to finalize the solution:
#(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))#
#m = (color(red)(5)/color(blue)(8))/(color(green)(1)/color(purple)(4)) = (color(red)(5) xx color(purple)(4))/(color(blue)(8) xx color(green)(1)) = 20/8 = (4 xx 5)/(4 xx 2) = (color(red)(cancel(color(black)(4))) xx 5)/(color(red)(cancel(color(black)(4))) xx 2) = 5/2#
The slope of the line passing through the two points is #m = 5/2#
