What is the equation of a line passing through (-3,7) with a slope of -1/5?

You are trying to find a line that has a general equation of
y  = mx + b
You know what m is because it is given as the slope.
m = - 1/5

y = - 1/5 x + b
Now to use the point to find b
y = 7
x = - 3

7 = -1/5 (-3) + b
7 = 3/5 + b look out for those nasty minus signs. There are 2 of them and they turn into plus.
7 - 3/5 = b
b = 6 2/5 = 6.4

Change m to -0.2
So y = -0.2 x + 6.4