![Tony B]()
Tony B
The graph of y=x-3y=x−3 is almost the same as y=xy=x. The difference is that every point on y=xy=x has been lowered by 3.
Thus, instead of the y-intercept being at y=0y=0 it is at y=-3y=−3 instead.
Consider the generic equation of y=mx+c color(white)(.)y=mx+c. where mm is the gradient (slope).
If you compare this to both y=xy=x and y=x-3y=x−3 you will observe that there is no value shown for mm. That is because it is there but it's value is 1 and it is good mathematical practice to NOT write 1x1x
The gradient of 1 =("count of up or down")/("count of along - left to right")=count of up or downcount 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=0x=0 so if we substitute the value of 0 for xx we get:
y=x-3" "->" "y=0-3y=x−3 → y=0−3
So at x=0x=0 we have y=-3y=−3
So the x-intercept is at the point P->(x,y)=(0,-3)P→(x,y)=(0,−3)
Similarly the graph crosses the x-axis at y=0y=0 so by substitution we have:
y=x-3" "->" "0=x-3y=x−3 → 0=x−3
Add 3 to both sides
0+3=x-3+30+3=x−3+3
3=x+03=x+0
x=3x=3
So the y-intercept is at the point P->(x,y)=(3,0)P→(x,y)=(3,0)
