Question

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

Answer 1

you'd use it becuase that's how you graph a line correctly.
the y intercept is where I would suggest you start and the use the slope or rate of change to find your next points on your line to graph the line.
but you'd use those two things to make sure your graphing to right line for your equation.

Answer 2

you would use the y-intercept and slope because y-intercept form is the easiest way to graph. you just plot the y-intercept and draw the line with the correct slope.