It is convenient to work with pairs of points on the graph from right to left.
Between 1 and 2, the graph goes over 4 and down 1, so the slope is -1/4
Between 0 and 1, the graph goes over 4 and down 2, so the slope is -2/4 = -1/2
We can see a trend here. For each unit interval farther to the left, the slope doubles. So, we have ...
1 ≤ x ≤ 2 : -0.25
0 ≤ x ≤ 1 : -0.5
-1 ≤ x ≤ 0 : -1
-2 ≤ x ≤ -1 : -2
The average slope over the longer intervals will be the average of the slopes in the (same length) intervals that make up the longer interval.
-2 ≤ x ≤ 0 : average of -2 and -1, so -1.5
0 ≤ x ≤ 2 : average of -0.5 and -0.25, so -0.375
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Going by the numbers on your list here, the matching (interval, slope) pairs are ... (1, 3), (2, 5), (3, 2), (4, 4), (5, 6), (6, 1)
