To find the slope we find the difference ∂y of the y coords and the difference ∂x of the x coords:
We can write the equation of the line y=mx+b, or y=-3x/2+b, where b is the y-intercept. To find b plug in either point, x=3, y=-1:
-1=-3*3/2+b; b=9/2-1=7/2, so y=-3x/2+7/2. The x-intercept is found by putting y=0: 3x/2=7/2 so x=7/3, the x-intercept. In slope intercept form we have: y-7/2=-(3/2)(x-7/3). This is the same as writing y=-3x/2+7/2.
CHECK Put x=3 and see if we get -1––we do; put x=-1 and see if we get 5––we do. So the answer seems OK.