Question

Why is the equation y=5x a special case of the slope-intercept form?

Answer 1

it passes through the origin (0,0)
normally the sllope intercpet form has something in b
y=mx+b
but now b=0 so this is unusual

Answer 2

It's a special case of the slope-intercept form because it is of the form y=mx

Generally, lines can be written in the form of y=mx+b, but in this case the b=0 which means it goes through the origin.

By the way, b is the y-intercept, and m is the slope.
y-intercept is when x=0

I have attached a graph of the line y=5x so you can understand it better.