Question

write an equation in slope - intercept to represent the relationship in the table

Answer 1

pick 2 random ascending x values and calculate the difference delta to get the slope
$\delta \: x = - 2 - ( - 1) = 1$
so your slope is "1"

and as you can see, that x=0 at y=3, so your y-intercept is 3
thats it, your function is
$f(x) = x + 3$