Have a look at https://socratic.org/s/aEw6Hquc
It uses different values but it has quite an extensive explanation.
Set point 1 as #_P_1->(x_1,y_1)=(-3/4,5/3)#
Set point 2 as #P_2->(x_2,y_2)=(1/3,2/5)#
When determining the gradient you read left to right on the x-axis
So as #x_1=-3/4# it comes before #x_2=+1/3#
So the change in #x# reading left to right is #x_2-x_1#
Also the change in #y# reading left to right on the x-axis is#color(white)(.) y_2-y_1#
Thus the gradient is:
#("change in y")/("change in x")->(y_2-y_1)/(x_2-x_1)=(2/5-5/3)/(1/3-(-3/4)) = (2/5-5/3)/(1/3+3/4)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider just the top (numerator) "->2/5-5/3)#
#color(green)([2/5color(red)(xx1)]-[5/3color(red)(xx1)]" "=" "[2/5color(red)(xx3/3)]-[5/3color(red)(xx5/5)]#
#" "color(green)(" "[6/15]-[25/15]#
#" "color(green)(-19/15)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider just the bottom (denominator) "->1/3+3/4)#
#color(green)([1/3color(red)(xx1)]+[3/4color(red)(xx1)]" "=" "[1/3color(red)(xx4/4)]+[3/4color(red)(xx3/3]]#
#" "color(green)([4/12]+[9/12]#
#" "color(green)(13/12)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#
#("change in y")/("change in x")" "=" "(color(white)(.)-19/15color(white)(.))/(13/12)#
This is the same as: #" "-19/15xx12/13 =- 1 11/65 -> -76/65#
Checking with a graph:
