first we want to get the equation in the form y = mx + b, once it is in this form, we know that the slope is m and the y-intercept is b.

x + y = 3

=> y = -x + 3 ...............subtracted x from both sides

now we have it in the correct form. we have a -1 in front of the x, so the slope of this line is -1. we also have a lone constant 3, this is our y-intercept