Why might someone choose to use the the y-intercept and the slope to graph a line?

For this case the generic equation of the line is given by:

y = mx + b

Where,

m: slope of the line

b: intersection with the y axis.

To graph a line it is necessary to know the values of m and b.

y = mx + b

You need to know m and b to graph the function completely.

For this reason, someone would choose to use the y-intercept and the slope