![Tony B]()
The graph of y=x-3 is almost the same as y=x. The difference is that every point on y=x has been lowered by 3.
Thus, instead of the y-intercept being at y=0 it is at y=-3 instead.
Consider the generic equation of y=mx+c color(white)(.) where m is the gradient (slope).
If you compare this to both y=x and y=x-3 you will observe that there is no value shown for m. That is because it is there but it's value is 1 and it is good mathematical practice to NOT write 1x
The gradient of 1 =("count of up or down")/("count of along - left to right")
This must mean that the (count of up or down) = (the count of along")
The y-axis passes through the x-axis at x=0 so if we substitute the value of 0 for x we get:
y=x-3" "->" "y=0-3
So at x=0 we have y=-3
So the x-intercept is at the point P->(x,y)=(0,-3)
Similarly the graph crosses the x-axis at y=0 so by substitution we have:
y=x-3" "->" "0=x-3
Add 3 to both sides
0+3=x-3+3
3=x+0
x=3
So the y-intercept is at the point P->(x,y)=(3,0)
