how do find the y and x intercepts for the equation 3x + y = -7 ?

The x- and y- intercepts are the points where the line intersects the axes, i.e. x=0, or y=0.

The y-intercept is obtained by setting x=0 and solving for y:
3(0) + y = -7
y=-7

Similarly, the x-intercept can be calculated by setting y=0:
3x + 0 = -7
x = -7/3