[tex]y=x[/tex] or [tex]x=y[/tex] is very easy to graph.
Choose whatever value of [tex]x[/tex] and use the same for [tex]y[/tex] in the same coordinate. Repeat and strike a line through all the points.
Some examples of valid points would be: [tex](1,1)[/tex], [tex](2,2)[/tex], [tex](0,0)[/tex] and [tex](-1,-1)[/tex].
Then, to graph [tex]y=4x-9[/tex] you have to look at it in terms of the equation of a line ([tex]y=mx+c[/tex]) and its parts.
In this case, [tex]m=4[/tex] and [tex]c=-9[/tex].
So, you choose any value for [tex]x[/tex] and you solve to find its [tex]y[/tex] counterpart.
I will start with [tex]x=0[/tex]:
[tex]x=0\\\\y=4(0)-9\\y=0-9\\y=-9[/tex]
Now, we have a first coordinate: [tex](0,-9)[/tex].
Repeat with a different value:
[tex]x=5\\\\y=4(5)-9\\y=20-9\\y=11[/tex]
It gives us the coordinates [tex](5,11)[/tex].
Plot those into the graph and strike a line through them.
Wherever the two lines in your Cartesian Plane cross, that is the solution for both equations. It should be [tex]3[/tex].
You can check it by replacing [tex]x[/tex] and [tex]y[/tex] by "3" in both formulas and equating the values of [tex]y[/tex]:
[tex]y=x\\y=4x-9\\\\x=4x-9\\(3)=4(3)-9\\3=12-9\\3=3[/tex]
Your solution is worked out and checked to be correct.
PS: I am attaching a picture of the graph, so you can have a visual idea of what it should look like.
