7x−y=9: positive or negative rate of change?
13x+y=2: positive or negative rate of change?
x: -4, -1, 2, 5, 8
y: -5, -3, -1, 1, 3 : positive or negative rate of change?

The general linear equation is in the form of y=mx+c where m is the slope or gradient... if m is negative, the rate of change is negative and if m is positive the rate of change is positive.

So firstly you need to rearrange the equations to get them in this form.

7x-y=9
7x=y+9
y=7x-9
Therefore this has a positive rate of change of 7

13x+y=2
y=-13x+2
Therefore this has a negative rate of change of -13

The last one is a little more difficult... we can get the gradient using two of these coordinates and using the formula of:
m=(y2-y1)/(x2-x1), where y2 is the y-coordinate of the second point, y1 is the y-coordinate of the first point, etc...
I'll use the points, (5, 1) and (8,3)
Therefore,
m=(3-1)/(8-5)
m=2/3
Therefore this has a positive gradient of 2/3

Hope all that helps :)