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.

Answer:

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

If someone had an equation that was in slope intercept form, the y intercept and slope are easily accessible and easily calculable.

Therefore, if someone had a line that was in slope intercept form, then they would probably choose to use the y intercept and slope to graph that line.