Okay, let's see...
First, find the slope by subtracting the first order pair's points from the second, and making the remainder of the y-values your numerator and the remainder of the x-values your numerator.
7-10=3
6-(-3)=9
Your slope is 3/9, or 1/3.
Our current equation is y=1/3x+b (b is the y-intercept).
Now, to find the intercept, we only need one point. Let's use (6, 7).
All we need to do is plug in the values. When we do that, we get...
7=1/3(6)+b
Now solve...
7=2+b
5=b
Now, we know that our y-intercept is b!
Our final equation is y=1/3x+5
In conclusion, the equation for a line with the points, (-3, 10) and (6, 7), is...
y=1/3x+5