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))m=y2−y1x2−x1
Where mm is the slope and (color(blue)(x_1, y_1)x1,y1) and (color(red)(x_2, y_2)x2,y2) 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=−112−5613−−32
m = (color(red)(-1/12) - color(blue)(5/6))/(color(red)(1/3) + color(blue)(3/2))m=−112−5613+32
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=−112−(22×56)(22×13)+(33×32)
m = (color(red)(-1/12) - color(blue)(10/12))/(color(red)(2/6) + color(blue)(9/6))m=−112−101226+96
m = (-11/12)/(11/6)m=−1112116
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))abcd=a×db×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 = -1−11121112=−11×1212×11=−132132=−1
