Afunction f(x) is graphed below what is the function rule in slope intercept form f(x) =

The general formula for a line is y=mx+c, where m is the gradient (slope) and c is the intercept.
We can extrapolate c from the graph directly - it intercepts the y axis at -1, so c has a value of -1.
The gradient can be calculated by determining what the y value changes by for each value of x. Since this evidently has a fraction gradient, it's easier to take whole numbers.
We can see a triangle with whole numbers - from (-3,0) to (0,-1). The difference in x is +3 and the difference in y is -1. Dividing these gives us -1/3.

Therefore, the gradient of the graph (i.e. m) is -1/3
Putting these together: