What's up?
y=x is your 'perfect' line. You should know how to graph that - just go 45 degrees from the origin in a north-east direction.
You can transform it in a number of ways:
1) You can change its slope
y=2x
The line is now twice as steep. For every unit you move in the x direction (across), you move up two in the y direction. Wheras y=x is move up one and across one. It is still in the north-east direction but it is more northerly now.
2) You can change its direction
This one is easy.
y=-x
This is the same line but instead of being north-east, it is north-west.
3) You can translate the line. This seems to be what you need help with.
y=x cuts the x-axis at (0,0) don't you agree? It also cuts the y-axis here.
What about y=2x? It is exactly the same. In general, y=ax where as is any number, cuts the x and y axes at (0,0).
What if we have y=x+1?
It cuts the x-axis when y=0. y=0=x+1 means x=-1. It cuts the y-axis when x=0 which is: y=1.
Right, so what is a translation?
A translation is when you add any number to the line:
y=x+1
y=3x+5
y=x-9
If you translate a line 1 unit to the right in the x direction, you've done the following:
y=x+1.
The general equation of the line:
y=ax+b
Any line can be formed from this. If you let a=1, b=0, you get:
y=x.
b is the translation, a is the slope. for y=x, a=1 because 1=1/1 or one unit up, one across. b=0 because y=x isn't translated at all.
For the line y=3x-9
a=3, b=-9
b is the translation, so y=3x-9 is moved LEFT along the x-axis by 0 units.
Finding the points of intersection:
x-intersection: when y=0: 3x-9=0 gives when x=3
y-intersection: when x=0: y=-9
Hope that helped in time.
