Slope or ' gradient ' is the amount of 'up' for 1 'along'.

So it is: #color(brown)(("change in y-axis")/("change in x-axis"))#

#color(white)(xxxxxx)color(brown)(= (y_2-y_1)/(x_2-x_1) )#

#color(blue)("You have "(x_1,y_1)-> (3/5,2))#

#color(blue)("and "color(white)(xxxx)color(blue)((x_2,y_2)-> (2/10,5/4))#

So #= (y_2-y_1)/(x_2-x_1) =(5/4 -2)/(2/10-3/5)#

#= (5/4 -8/4)/(1/5-3/5)#

#=(-3/4)/(-2/5)#

This is the same as #(-3/4) divide (-2/5)#

Same as #(-3/4) times (-5/2) = +15/8#

#color(red)("Note that (negative) "divide" (negative) = (positive)")#

So for every 8 along you go 15 up ...... ( the gradient)

Or #( 15 divide 8 )/(8 divide 8) = (1.875)/1#

## #color(green)("For every 1 along you go up 1.875")#