First, we must find the equation of the given line. The slope is "rise over run," or the change in y over the change in x from one point to another.
The two points shown are (0,-1) and (3,1). In these points, y increases by 2. This means the change in y is 2. In these points, x increase by 3. This means the change in x is 3. Thus, the change in y over change in x is 2/3. This means that the slop of the given line is 2/3.
In the form y=mx+b, where m is the slope, b is the y intercept. This is because the y intercept occurs when x is 0. If x is zero, mx is zero, so y=b. In other words, when x equals 0, y=b. This creates the point (0,b), which is the y-intercept. Since the y-intercept of the given line is -3, the equation for this line is: y=2/3x-3.
A line parallel to this will need to have the same slope. This allows us to eliminate choices C and D, which do not have the same slope.
In order for the line to have an x-intercept of (-3,0), y must equal 0 when x is -3, since ordered pairs are (x,y). We can solve the equation using the information we know:
0=((2/3)(-3))+b
This is because we know the slope is 2/3, and that when x is -3, y is 0.
Then, we can solve from there:
0=(-2)+b (just multiply 2/3 and -3)
2=b (add 2 to both sides)
Thus, the correct equation is:
B) y=2/3x+2
