Passes through (7, 6) and (10, 15)

y=mx+b

y is dependant, m is slope, x is independant, b is vertical shift

The equation for finding a slope is (Y1-y2)/(X1-X2).

(15-6)/(10-7)=9/3=3  so the slope is 3

y=3x+b

To find b, substitute an instance of y and x, for y and x.  You can use 15 and 10 or 6 and 7, both give the same answer

15 and 10:
15=3(10)+b
15=30+b
-15=b

6 and 7
6=3(7)+b
6=21+b
-15=b

see?

so b=-15, and the formula is 

y=3x-15.

The graph looks like 

Note that the line crosses the vertical (y) axis at -15, b.