hi
let take two points :
( 0; -1) and (4 ; 2)
here is a = 0 ; f(a) = -1
b = 4 ; f(b) = 2
Slope is : f(a) -f(b) / a-b
let's apply : -1 - 2 / 0-4 = -3/-4 = 3/4
Slope is 3/4
if you want to check result, you can calculate the coordonate of an other point and see if it match.
here I read that there is a point on the line for -4 ; -4
here I can read that Y axis value for X = 0 is -1
as a line is defined by : mx+p
with m = slope and p value for x = 0
so : p = - 1
with m = 3/4 ; x = -4 and p = -1
I can test my line equation and see if it match the result :
3/4 ( -4) - 1 = -12/4 - 1 = -3 -1 = -4
Result match what I see on the graph, so previous result is correct.
: Slope is 3/4
ps : if line grows, the slope can only be positive. if line decrease, slope is negative, if line is constant, then slope is still and equal 0