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)_P1→(x1,y1)=(−34,53)
Set point 2 as P_2->(x_2,y_2)=(1/3,2/5)P2→(x2,y2)=(13,25)
When determining the gradient you read left to right on the x-axis
So as x_1=-3/4x1=−34 it comes before x_2=+1/3x2=+13
So the change in xx reading left to right is x_2-x_1x2−x1
Also the change in yy reading left to right on the x-axis iscolor(white)(.) y_2-y_1.y2−y1
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)change in ychange in x→y2−y1x2−x1=25−5313−(−34)=25−5313+34
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color(blue)("Consider just the top (numerator) "->2/5-5/3)Consider just the top (numerator) →25−53
color(green)([2/5color(red)(xx1)]-[5/3color(red)(xx1)]" "=" "[2/5color(red)(xx3/3)]-[5/3color(red)(xx5/5)][25×1]−[53×1] = [25×33]−[53×55]
" "color(green)(" "[6/15]-[25/15] [615]−[2515]
" "color(green)(-19/15) −1915
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Consider just the bottom (denominator) "->1/3+3/4)Consider just the bottom (denominator) →13+34
color(green)([1/3color(red)(xx1)]+[3/4color(red)(xx1)]" "=" "[1/3color(red)(xx4/4)]+[3/4color(red)(xx3/3]][13×1]+[34×1] = [13×44]+[34×33]
" "color(green)([4/12]+[9/12] [412]+[912]
" "color(green)(13/12) 1312
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Putting it all together")Putting it all together
("change in y")/("change in x")" "=" "(color(white)(.)-19/15color(white)(.))/(13/12)change in ychange in x = .−1915.1312
This is the same as: " "-19/15xx12/13 =- 1 11/65 -> -76/65 −1915×1213=−11165→−7665
Checking with a graph:
![Tony B]()
