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So you correctly wrote that the slope is represented by Δy/Δx. The Greek capital letter delta means "change in," so we are looking at the change in y divided by the change in x. You might also hear this called "rise over run," because change in y is the vertical change (rise) and change in x is the horizontal change (run).
Now, to find the change in y and x, we need to take two points,
and 
. We can then find the slope, m, as below:
So, as we're asked to state the slope and the behavior of the graph. Generally, if you see that as x increases, y increases, then the slope is positive. If y decreases, then the slope is negative. If y stays the same (constant), then the slope is zero. If x is constant, then the slope is undefined. Unfortunately, this worksheet also asks us to calculate the slope. So the equation above comes in handy!
1) let's take x = -1, y = -5 and x = 0, y = 3. We can write
and 
(we can choose either point to be 
so long as we're consistent.
This is a positive (+) change.
2)
Negative (–).
3)
Positive (+).
4)
Positive (+).
5)
Negative (–).
Now, to find the change in y and x, we need to take two points,
So, as we're asked to state the slope and the behavior of the graph. Generally, if you see that as x increases, y increases, then the slope is positive. If y decreases, then the slope is negative. If y stays the same (constant), then the slope is zero. If x is constant, then the slope is undefined. Unfortunately, this worksheet also asks us to calculate the slope. So the equation above comes in handy!
1) let's take x = -1, y = -5 and x = 0, y = 3. We can write
This is a positive (+) change.
2)
Negative (–).
3)
Positive (+).
4)
Positive (+).
5)
Negative (–).