You can substitute anything for x. For example, for x = 1 we have y = -5, and for x = 6 we have y = 0. So, the points (1, -5) and (6, 0) belong to the graph.
Hello everyone. I am having trouble understanding something and was wondering if someone could help me.
We are doing Graphs of Linear Equations and I am in the world of hurt. I am taking this class on line and I don't think I know what I am doing.
Problem
y = x - 6
I need to find some ordered pairs that are solutions so I can graph it on the graph.
My problem is not understanding this is how do you know what will work to be the right answer. I mean you clearly have to substitute a number for x then work it in the problem.
But like I said I am having trouble finding the right substitution to replace x in the problem.
I NEED HELP, PLEASE SOMEONE?
You can substitute any number for x.
That is a linear equation so it makes a line.
The x and y in the equation represent all of the ordered pairs (points) that create line.
Every ordered pair (point) on your line should work to make that statement true.
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For example:
y = x - 6
plug in 7 for x
and get 1 for y
So ordered pair (7,1) is a point on your line.
Plug in 3 for x
and get -3 for y
So ordered pair (3, -3) is a point on your line as well.
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Why can you plug any number you want in for x?
Linear equations create lines, and one of the traits of these lines is that they go from left to right forever and ever. They don't necessarily go up and down forever and ever.
So, because they move from left to right forever, this means they travel along the x-axis in both directions touching every x-coordinate. They also never stop, or turn around so these lines will touch each and every x-coordinate only once. So there is literally an x-coordinate represented by every never in existence.
This means if you are trying to find an ordered you can just plug any number you want in for x and when you solve you will find the y-coordinate that matches up with it to create a point that exists on your line. Again, you can choose ANY number for x, because every linear equation's line touches every x-coordinate on the x-axis by moving left and right forever.
This same concept applies to equations of curves and waves as they also move left and right forever, but not necessarily up and down forever. So you cannot just choose a random number for y, as often times your choices are limited. For example:
The equation for a basic curve would be y = x^2
If you graph that you will notice the curve never touches any negative numbers on the why axis. You will also notice that no matter what you plug in for x, you will never get a negative answer for that very reason. So this is why x is known as the input, because all of these special equations (functions) move left and right forever, but not up and down.